A graph is called s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular cyclic or elementary abelian coverings of the Petersen graph for each s ≥ 1 are classified w...A graph is called s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular cyclic or elementary abelian coverings of the Petersen graph for each s ≥ 1 are classified when the fibre-preserving automorphism groups act arc-transitively.As an application of these results, all s-regular cubic graphs of order 10p or 10p2 are also classified for each s ≥ 1 and each prime p, of which the proof depends on the classification of finite simple groups.展开更多
Based on Petersen graph, a new interconnection network, the RP(k) network, is devel-oped and the properties of the RP(k) network are investigated. The diameter of the RP(k) network is [ k/2] + 2 and its degree is 5. W...Based on Petersen graph, a new interconnection network, the RP(k) network, is devel-oped and the properties of the RP(k) network are investigated. The diameter of the RP(k) network is [ k/2] + 2 and its degree is 5. We prove that the diameter of the RP(k) network is much smaller than that of the 2-D Torus network when the number of nodes in interconnection networks is less than or equal to 300. In order to analyze the communication performance in a group of nodes, we propose the concepts of the optimal node groups and the diameter of the optimal node groups. We also show that the diameter of the optimal node groups in the RP(k) network is less than that in the 2-D Torus net-work. Especially when the number of nodes in an optimal node group is between 6 and 100, the diam-eter of the optimal node groups in the RP(k) network is half of that in the 2-D Torus network. Further-more based on the RP(k) network we design a set of routing algorithms which are point-to-point rout-ing, permutation routing, one-to-all routing and all-to-all routing. Their communication efficiencies are [ k/2] +2, k + 5, [k/2] + 2, and k + 5 respectively. The RP(k) network and the routing algorithms can provide efficient communication means for parallel and distributed computer system.展开更多
Generalized Petersen graphs iare an important class of commonly used in-terconnection networks and have been studied by various researchers. In this paper, weshow that the diameter of generalized Petersen graph P(m, 2...Generalized Petersen graphs iare an important class of commonly used in-terconnection networks and have been studied by various researchers. In this paper, weshow that the diameter of generalized Petersen graph P(m, 2) is O(m/4) and the 3-widediameter of P(m, 2) is O(m/3).展开更多
The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994.However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are supe...The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994.However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-graceful. A conjecture is proposed.展开更多
Sortilin was discovered in 1997 by Petersen and his colleagues.The single transmembrane receptor was isolated as a 95 kDa membrane glycoprotein by receptor-associated protein affinity chromatography and therefore init...Sortilin was discovered in 1997 by Petersen and his colleagues.The single transmembrane receptor was isolated as a 95 kDa membrane glycoprotein by receptor-associated protein affinity chromatography and therefore initially named gp95.The cDNA library screening revealed sequence homology between the luminal segment of gp95/sortilin and the yeast vacuolar sorting protein 10 protein(Vps10p)domain(Petersen et al.,1997).The Vps10p domain was first identified in the Saccharomyces cerevisiae protein Vps10p that directs lysosomal enzymes from the Golgi to the vacuole(Marcusson et al.,1994).展开更多
Intestinal occlusion by internal hernia is not a rare complication(0.2%-5%)after Laparoscopic Roux-en-Y-GBP(LGBP)with higher morbidity and mortality related to mesenteric vessels involvement.In our Center,from October...Intestinal occlusion by internal hernia is not a rare complication(0.2%-5%)after Laparoscopic Roux-en-Y-GBP(LGBP)with higher morbidity and mortality related to mesenteric vessels involvement.In our Center,from October 2009 to April 2013 we have had 17 pts treated for internal hernia on 412 LGBP(4.12%).Clinical case:28-year-old woman,operated of LGBP(BMI=49;comorbidity:diabetes mellitus and arthropathy)about 10mo before,was affected by recurrent abdominal pain with alvus alteration lasting for a week.After vomiting,she went to first aid Unit of a peripheric hospital where she made blood tests,RX and US of abdomen that resulted normal so she was discharged with flu like syndrome diagnosis.After 3 d the patient contacted our Center since her symptoms got worse and was hospitalized.Blood tests showed an alteration of hepatic enzymes and amylases.The abdominal computed tomography(CT)showed the presence of fluid in perisplenic,peri-hepatic areas and in pelvis and a"target like imagine"of"clustered ileal loops"with a superior mesenteric vein(SMV)thrombosis involving the Portal Vein.During the operation,we found a necrosis of80 cm of ileus(about 50 cm downstream the jejuno-jejunal anastomosis)due to an internal hernia through Petersen’s space causing a SMV thrombosis.The necrotic bowel was removed,the internal hernia was reduced and Petersen’space was sutured by not-absorbable running suture.An anticoagulant therapy was begun in the post-operative time and the patient was discharged after 28 d.Conclusions:The internal hernia diagnosis is rarely confirmed by preoperative exams and it is obtained in most cases by laparoscopy but the improvement of technologies and the discover of"new"CT signs interpretation can address to an early laparoscopic treatment for high suspicion cases.展开更多
The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we st...The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity.展开更多
The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. In this paper, we determine the skewness of the generalized Petersen graph P（4k, k） and hence a lower bound for ...The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. In this paper, we determine the skewness of the generalized Petersen graph P（4k, k） and hence a lower bound for the crossing number of P（4k, k）. In addition, an upper bound for the crossing number of P（4k, k） is also given.展开更多
A graphG is supereulerian if G has a spanning eulerian subgraph.Boesch et al.[J.Graph Theory,1,79–84（1977）]proposed the problem of characterizing supereulerian graphs.In this paper,we prove that any 3-edge-connecte...A graphG is supereulerian if G has a spanning eulerian subgraph.Boesch et al.[J.Graph Theory,1,79–84（1977）]proposed the problem of characterizing supereulerian graphs.In this paper,we prove that any 3-edge-connected graph with at most 11 edge-cuts of size 3 is supereulerian if and only if it cannot be contractible to the Petersen graph.This extends a former result of Catlin and Lai[J.Combin.Theory,Ser.B,66,123–139（1996）].展开更多
A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the qual...A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the quality of a book embedding which is the minimum number of pages in which the graph G can be embedded. In this paper, the authors discuss the embedding of the generalized Petersen graph and determine that the page number of the generalized Petersen graph is three in some situations, which is best possible.展开更多
A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χ...A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.展开更多
The generalized Petersen graphs p(n,k) n≥3, 1≤k<n/2, consist of an outer n-cycle x0x1 x2'''xn--1 , a set of n spokes x,yi (O≤i≤n--1), and n inner edges yiyi+k with indices taken modulo n.This paper ...The generalized Petersen graphs p(n,k) n≥3, 1≤k<n/2, consist of an outer n-cycle x0x1 x2'''xn--1 , a set of n spokes x,yi (O≤i≤n--1), and n inner edges yiyi+k with indices taken modulo n.This paper deals with (a,b)-consecutive labelings of generalized Petersen graph p(n,k).展开更多
This paper first investigates the topological properties of RP(k) networks. Then focusing on the embedding of rings and 2-D meshes into the RP(k) network, it is proved that the RP(k) network is a Hamiltonian graph and...This paper first investigates the topological properties of RP(k) networks. Then focusing on the embedding of rings and 2-D meshes into the RP(k) network, it is proved that the RP(k) network is a Hamiltonian graph and the ring with 10*k nodes can be embedded into the RP(k) network with load, expansion, dilation and congestion all equal to 1. If there exists a faulty node on each slice in the RP(k) network, throwing off the faulty nodes, the RP-1(k) network is obtained. It is also proved that there exists a Hamiltonain cycle in the RP-1(k) network. So the ring with 9*k nodes can be embedded into the RP- 1(k) network. After that, we discuss the embedding of a 2-D mesh, M1(a, b), into the RP(k) network. By defining the sequence-column-order mapping, the snake-like-column-order mapping and the shortest path mapping, we obtain two ways of embedding a 2-D mesh into the RP(k) network. The performances of the embedding are as follows. In the snake-like-column-order mapping, the dilations are 1, 2, 3, 3 and 2 and the congestion are 1, 3, 4, 5 and 3 respectively when a is equal to 1, 2, 3, 4 and 5. In the sequence- column-order mapping, the dilation is equal to 3 and the congestion is equal to 6 when a is between 6 and 9. The dilation is equal to a/10+2 and the congestion is equal to max{ a/10+1, 6} when a >10. As a special case, the four parameters are also equal to 1 when a is equal to 10.展开更多
In the paper, we prove that for every integer n ≥ 1, there exists a Petersen power pn with nonorientable genus and Euler genus precisely n, which improves the upper bound of Mohar and Vodopivec＇s result [J. Graph Th...In the paper, we prove that for every integer n ≥ 1, there exists a Petersen power pn with nonorientable genus and Euler genus precisely n, which improves the upper bound of Mohar and Vodopivec＇s result [J. Graph Theory, 67, 1-8 （2011）] that for every integer k （2 ≤ k ≤ n- 1）, a Petersen power Pn exists with nonorientable genus and Euler genus precisely k.展开更多
Let G be a graph and k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of G with a set of k colors. In every turn, one vertex will be chosen by one playe...Let G be a graph and k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of G with a set of k colors. In every turn, one vertex will be chosen by one player. Alice’s goal is to color all vertices with the k colors, while Bob’s goal is to prevent her. The game chromatic number denoted by?χg(G), is the smallest k such that Alice has a winning strategy with k colors. In this paper, we determine the game chromatic number?χg of circulant graphs?Cn(1,2), , and generalized Petersen graphs GP(n,2), GP(n,3).展开更多
Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied . The total domination number of generalized Petersen graphs P(m,2) is obtained in this paper.
Both the circulant graph and the generalized Petersen graph are important types of graphs in graph theory. In this paper, the structures of embeddings of circulant graph C（2n ＋ 1; {1, n}） on the projective plane ar...Both the circulant graph and the generalized Petersen graph are important types of graphs in graph theory. In this paper, the structures of embeddings of circulant graph C（2n ＋ 1; {1, n}） on the projective plane are described, the number of embeddings of C（2n ＋ 1; {1, n}） on the projective plane follows, then the number of embeddings of the generalized Petersen graph P（2n ＋ 1, n） on the projective plane is deduced from that of C（2n ＋ 1; {1, n}）, because C（2n ＋ 1; {1, n}） is a minor of P（2n ＋ 1, n）, their structures of embeddings have relations. In the same way, the number of embeddings of the generalized Petersen graph P（2n, 2） on the projective plane is also obtained.展开更多
Generalized Petersen graphs are commonly used interconnection networks, and wide diameter is an important parameter to measure fault-tolerance and efficiency of parallel processing computer networks. In this paper, we...Generalized Petersen graphs are commonly used interconnection networks, and wide diameter is an important parameter to measure fault-tolerance and efficiency of parallel processing computer networks. In this paper, we show that the diameter and 3-wide diameter of generalized Petersen graph P（rn, a） are both O（m/2a）, where a ≥ 3.展开更多
In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） a...In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P（n, 4） has constant metric dimension.展开更多
基金suppeorted by the National Natural Science Foundation ofChina(Grant No.10571013)the Key Project of Chinese Ministry of Education Com2 Mac-KOSEF in Korea(Grant No.R11-1999-054).
文摘A graph is called s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular cyclic or elementary abelian coverings of the Petersen graph for each s ≥ 1 are classified when the fibre-preserving automorphism groups act arc-transitively.As an application of these results, all s-regular cubic graphs of order 10p or 10p2 are also classified for each s ≥ 1 and each prime p, of which the proof depends on the classification of finite simple groups.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69933020) National High Performance Computing Fund.
文摘Based on Petersen graph, a new interconnection network, the RP(k) network, is devel-oped and the properties of the RP(k) network are investigated. The diameter of the RP(k) network is [ k/2] + 2 and its degree is 5. We prove that the diameter of the RP(k) network is much smaller than that of the 2-D Torus network when the number of nodes in interconnection networks is less than or equal to 300. In order to analyze the communication performance in a group of nodes, we propose the concepts of the optimal node groups and the diameter of the optimal node groups. We also show that the diameter of the optimal node groups in the RP(k) network is less than that in the 2-D Torus net-work. Especially when the number of nodes in an optimal node group is between 6 and 100, the diam-eter of the optimal node groups in the RP(k) network is half of that in the 2-D Torus network. Further-more based on the RP(k) network we design a set of routing algorithms which are point-to-point rout-ing, permutation routing, one-to-all routing and all-to-all routing. Their communication efficiencies are [ k/2] +2, k + 5, [k/2] + 2, and k + 5 respectively. The RP(k) network and the routing algorithms can provide efficient communication means for parallel and distributed computer system.
基金Supported by NNSF of China(10271114)and(INNSF of China (10301031)
文摘Generalized Petersen graphs iare an important class of commonly used in-terconnection networks and have been studied by various researchers. In this paper, weshow that the diameter of generalized Petersen graph P(m, 2) is O(m/4) and the 3-widediameter of P(m, 2) is O(m/3).
基金Partially supported by Faculty-Research Grant,Hong Kong Baptist University
文摘The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994.However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-graceful. A conjecture is proposed.
基金funding from the Research Initiative on Brain Barriers and Drug Delivery funded by the Lundbeck Foundation(grant No.2013-14113)。
文摘Sortilin was discovered in 1997 by Petersen and his colleagues.The single transmembrane receptor was isolated as a 95 kDa membrane glycoprotein by receptor-associated protein affinity chromatography and therefore initially named gp95.The cDNA library screening revealed sequence homology between the luminal segment of gp95/sortilin and the yeast vacuolar sorting protein 10 protein(Vps10p)domain(Petersen et al.,1997).The Vps10p domain was first identified in the Saccharomyces cerevisiae protein Vps10p that directs lysosomal enzymes from the Golgi to the vacuole(Marcusson et al.,1994).
文摘Intestinal occlusion by internal hernia is not a rare complication(0.2%-5%)after Laparoscopic Roux-en-Y-GBP(LGBP)with higher morbidity and mortality related to mesenteric vessels involvement.In our Center,from October 2009 to April 2013 we have had 17 pts treated for internal hernia on 412 LGBP(4.12%).Clinical case:28-year-old woman,operated of LGBP(BMI=49;comorbidity:diabetes mellitus and arthropathy)about 10mo before,was affected by recurrent abdominal pain with alvus alteration lasting for a week.After vomiting,she went to first aid Unit of a peripheric hospital where she made blood tests,RX and US of abdomen that resulted normal so she was discharged with flu like syndrome diagnosis.After 3 d the patient contacted our Center since her symptoms got worse and was hospitalized.Blood tests showed an alteration of hepatic enzymes and amylases.The abdominal computed tomography(CT)showed the presence of fluid in perisplenic,peri-hepatic areas and in pelvis and a"target like imagine"of"clustered ileal loops"with a superior mesenteric vein(SMV)thrombosis involving the Portal Vein.During the operation,we found a necrosis of80 cm of ileus(about 50 cm downstream the jejuno-jejunal anastomosis)due to an internal hernia through Petersen’s space causing a SMV thrombosis.The necrotic bowel was removed,the internal hernia was reduced and Petersen’space was sutured by not-absorbable running suture.An anticoagulant therapy was begun in the post-operative time and the patient was discharged after 28 d.Conclusions:The internal hernia diagnosis is rarely confirmed by preoperative exams and it is obtained in most cases by laparoscopy but the improvement of technologies and the discover of"new"CT signs interpretation can address to an early laparoscopic treatment for high suspicion cases.
基金funded by the Deanship of Scientific Research at Jouf University under Grant No.DSR-2021-03-0301supported by the Higher Education Commission of Pakistan through the National Research Program for Universities Grant No.20-16188/NRPU/R&D/HEC/20212021.
文摘The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity.
文摘The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. In this paper, we determine the skewness of the generalized Petersen graph P（4k, k） and hence a lower bound for the crossing number of P（4k, k）. In addition, an upper bound for the crossing number of P（4k, k） is also given.
基金Supported by National Natural Science Foundation of China(Grant No.11001287)Science Foundation Chongqing Education Committee(Grant Nos.KJ100725 and KJ120731)
文摘A graphG is supereulerian if G has a spanning eulerian subgraph.Boesch et al.[J.Graph Theory,1,79–84（1977）]proposed the problem of characterizing supereulerian graphs.In this paper,we prove that any 3-edge-connected graph with at most 11 edge-cuts of size 3 is supereulerian if and only if it cannot be contractible to the Petersen graph.This extends a former result of Catlin and Lai[J.Combin.Theory,Ser.B,66,123–139（1996）].
基金supported by the National Natural Science Foundation of China(Nos.11531010,11401510,11501487)the Key Laboratory Project of Xinjiang(No.2015KL019)the Doctoral Fund of Xinjiang University(No.BS150208)
文摘A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the quality of a book embedding which is the minimum number of pages in which the graph G can be embedded. In this paper, the authors discuss the embedding of the generalized Petersen graph and determine that the page number of the generalized Petersen graph is three in some situations, which is best possible.
文摘A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.
文摘The generalized Petersen graphs p(n,k) n≥3, 1≤k<n/2, consist of an outer n-cycle x0x1 x2'''xn--1 , a set of n spokes x,yi (O≤i≤n--1), and n inner edges yiyi+k with indices taken modulo n.This paper deals with (a,b)-consecutive labelings of generalized Petersen graph p(n,k).
文摘This paper first investigates the topological properties of RP(k) networks. Then focusing on the embedding of rings and 2-D meshes into the RP(k) network, it is proved that the RP(k) network is a Hamiltonian graph and the ring with 10*k nodes can be embedded into the RP(k) network with load, expansion, dilation and congestion all equal to 1. If there exists a faulty node on each slice in the RP(k) network, throwing off the faulty nodes, the RP-1(k) network is obtained. It is also proved that there exists a Hamiltonain cycle in the RP-1(k) network. So the ring with 9*k nodes can be embedded into the RP- 1(k) network. After that, we discuss the embedding of a 2-D mesh, M1(a, b), into the RP(k) network. By defining the sequence-column-order mapping, the snake-like-column-order mapping and the shortest path mapping, we obtain two ways of embedding a 2-D mesh into the RP(k) network. The performances of the embedding are as follows. In the snake-like-column-order mapping, the dilations are 1, 2, 3, 3 and 2 and the congestion are 1, 3, 4, 5 and 3 respectively when a is equal to 1, 2, 3, 4 and 5. In the sequence- column-order mapping, the dilation is equal to 3 and the congestion is equal to 6 when a is between 6 and 9. The dilation is equal to a/10+2 and the congestion is equal to max{ a/10+1, 6} when a >10. As a special case, the four parameters are also equal to 1 when a is equal to 10.
基金supported by the Fundamental Research Funds for the Central Universities(Grand No.NZ2015106)supported by National Natural Science Foundation of China(Grant Nos.11471106 and 11371133)NSFC of Hu’nan(Grant No.14JJ2043)
文摘In the paper, we prove that for every integer n ≥ 1, there exists a Petersen power pn with nonorientable genus and Euler genus precisely n, which improves the upper bound of Mohar and Vodopivec＇s result [J. Graph Theory, 67, 1-8 （2011）] that for every integer k （2 ≤ k ≤ n- 1）, a Petersen power Pn exists with nonorientable genus and Euler genus precisely k.
文摘Let G be a graph and k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of G with a set of k colors. In every turn, one vertex will be chosen by one player. Alice’s goal is to color all vertices with the k colors, while Bob’s goal is to prevent her. The game chromatic number denoted by?χg(G), is the smallest k such that Alice has a winning strategy with k colors. In this paper, we determine the game chromatic number?χg of circulant graphs?Cn(1,2), , and generalized Petersen graphs GP(n,2), GP(n,3).
文摘Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied . The total domination number of generalized Petersen graphs P(m,2) is obtained in this paper.
文摘Both the circulant graph and the generalized Petersen graph are important types of graphs in graph theory. In this paper, the structures of embeddings of circulant graph C（2n ＋ 1; {1, n}） on the projective plane are described, the number of embeddings of C（2n ＋ 1; {1, n}） on the projective plane follows, then the number of embeddings of the generalized Petersen graph P（2n ＋ 1, n） on the projective plane is deduced from that of C（2n ＋ 1; {1, n}）, because C（2n ＋ 1; {1, n}） is a minor of P（2n ＋ 1, n）, their structures of embeddings have relations. In the same way, the number of embeddings of the generalized Petersen graph P（2n, 2） on the projective plane is also obtained.
基金Supported by the National Natural Science Foundation of China (Grant No. 60973014)the Excellent Young Teachers Program of Shanghai Municipal Education Conmision (Grant No. B-8101-07-0027)Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200801411073)
文摘Generalized Petersen graphs are commonly used interconnection networks, and wide diameter is an important parameter to measure fault-tolerance and efficiency of parallel processing computer networks. In this paper, we show that the diameter and 3-wide diameter of generalized Petersen graph P（rn, a） are both O（m/2a）, where a ≥ 3.
文摘In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P（n, 4） has constant metric dimension.
