This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of ...This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face, and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s that appears in the graph. The paper examines the existence of such labelings for disjoint union of plane graphs.展开更多
This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a s...This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph. The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.展开更多
An （a, d）-edge-antimagic total labeling of a graph G is a bijection f from V（G） ∪ E（G） onto {1, 2,..., ｜V（G）｜ ＋ ｜E（G）｜} with the property that the edge-weight set {f（x） ＋ f（xy） ＋ f（y） ｜ xy ∈ ...An （a, d）-edge-antimagic total labeling of a graph G is a bijection f from V（G） ∪ E（G） onto {1, 2,..., ｜V（G）｜ ＋ ｜E（G）｜} with the property that the edge-weight set {f（x） ＋ f（xy） ＋ f（y） ｜ xy ∈ E（G）} is equal to {a, a ＋ d, a ＋ 2d,... ,a ＋ （｜E（G）｜ - 1）d} for two integers a 〉 0 and d ≥ 0. An （a,d）-edge- antimagic total labeling is called super if the smMlest possible labels appear on the vertices. In this paper, we completely settle the problem of the super （a, d）-edge-antimagic total labeling of the complete bipartite graph [（m,n and obtain the following results： the graph t（m,n has a super （a, d）-edge-antimagic total labeling if and only if either （i） m = 1, n = 1, and d ≥ 0, or （ii） m = 1, n≥2 （orn=1 and m≥2）,and d ∈{0,1,2},or （iii） m=l,n=2 （orn=1 and m = 2）, and d= 3, or （iv） m,n≥2, and d=1展开更多
Cayley graphs have many good properties as models of communication networks. This study analyzes the reliability of the Cayley graph based on the dihedral graph. Graph theory and analyses show that almost all Cayley g...Cayley graphs have many good properties as models of communication networks. This study analyzes the reliability of the Cayley graph based on the dihedral graph. Graph theory and analyses show that almost all Cayley graphs of the dihedral graph D2n are optimal super-λ. The number Ni（G） of cutsets of size i, λ≤ i≤λ＇ is given as Ni（G） = n[^（n-1）δ i-δ].展开更多
Researchers utilize information from the geoscience literature to deduce the regional or global geological evolution.Traditionally this process has relied on the labor of researchers.As the number of papers continues ...Researchers utilize information from the geoscience literature to deduce the regional or global geological evolution.Traditionally this process has relied on the labor of researchers.As the number of papers continues to increase,acquiring domain-specific knowledge becomes a heavy burden.Knowledge Graph(KG)is proposed as a new knowledge representation technology to change this situation.However,the super relation is not considered in the previous KG,which bridges the geological phenomenon(fact)and its precondition(condition).For instance,in the statement(“the late Archean was a crucial transition period in the history of global geodynamics”),the condition statement(“crucial transition for global geodynamics”)works as the complementary fact statement(“the late Archean was a crucial transition period”),which defines the scale of crucial transition accurately in the late Archean.In this study,fact-condition statement extraction is introduced to construct a geological knowledge graph.A rule-based multi-input multi-output model(R-MIMO)is proposed for information extraction.In the R-MIMO,fact-condition statements and their super relation are considered and extracted for the first time.To verify its performances,a GeothCF dataset with 1455 fact tuples and 789 condition tuples is constructed.In experiments,the R-MIMO model achieves the best performance by using BERT as encoder and LSTM-d as decoder,achieving F180.24%in tuple extraction and F170.03%in tag prediction task.Furthermore,the geothermic KG with super relation is automatically constructed for the first time by trained R-MIMO,which can provide structured data for further geothermic research.展开更多
Let G be a connected graph with vertex-set V(G)and edge-set E(G).A subset F of E(G)is an s-restricted edge-cut of G if G-F is disconnected and every component of G-F has at least s vertices.Letλs(G)be the minimum siz...Let G be a connected graph with vertex-set V(G)and edge-set E(G).A subset F of E(G)is an s-restricted edge-cut of G if G-F is disconnected and every component of G-F has at least s vertices.Letλs(G)be the minimum size of all s-restricted edge-cuts of G andξs(G)=min{|[X,V(G)\X]|:|X|=s,G[X]is connected},where[X,V(G)\X]is the set of edges with exactly one end in X.A graph G with an s-restricted edge-cut is called super s-restricted edge-connected,in short super-λs,ifλs(G)=ξs(G)and every minimum s-restricted edge-cut of G isolates one component G[X]with|X|=s.It is proved in this paper that a connected vertex-transitive graph G with degree k>5 and girth g>5 is super-λs for any positive integer s with s 2g or s 10 if k=g=6.展开更多
The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, ...The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, the graph Kuratowski-Mosco convergence and D-convergence of fuzzy (super) pramart and quasi-martingale are studied.展开更多
文摘This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face, and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s that appears in the graph. The paper examines the existence of such labelings for disjoint union of plane graphs.
文摘This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph. The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.
文摘An （a, d）-edge-antimagic total labeling of a graph G is a bijection f from V（G） ∪ E（G） onto {1, 2,..., ｜V（G）｜ ＋ ｜E（G）｜} with the property that the edge-weight set {f（x） ＋ f（xy） ＋ f（y） ｜ xy ∈ E（G）} is equal to {a, a ＋ d, a ＋ 2d,... ,a ＋ （｜E（G）｜ - 1）d} for two integers a 〉 0 and d ≥ 0. An （a,d）-edge- antimagic total labeling is called super if the smMlest possible labels appear on the vertices. In this paper, we completely settle the problem of the super （a, d）-edge-antimagic total labeling of the complete bipartite graph [（m,n and obtain the following results： the graph t（m,n has a super （a, d）-edge-antimagic total labeling if and only if either （i） m = 1, n = 1, and d ≥ 0, or （ii） m = 1, n≥2 （orn=1 and m≥2）,and d ∈{0,1,2},or （iii） m=l,n=2 （orn=1 and m = 2）, and d= 3, or （iv） m,n≥2, and d=1
基金Supported by the National Key Basic Research and Development (973) Program of China(No. 2007CB311003)
文摘Cayley graphs have many good properties as models of communication networks. This study analyzes the reliability of the Cayley graph based on the dihedral graph. Graph theory and analyses show that almost all Cayley graphs of the dihedral graph D2n are optimal super-λ. The number Ni（G） of cutsets of size i, λ≤ i≤λ＇ is given as Ni（G） = n[^（n-1）δ i-δ].
基金supported in part by the National Natural Science Foundation of China(NSFC)(No.61972365,42071382)in part by the CCF-NSFOCUS Kun-Peng Scientific Research Fund(CCFNSFOCUS 2021002)+1 种基金in part by the Natural Science Foundation of Hubei Province,China(No.2020CFB752)in part by the Open Research Project of the Hubei Key Laboratory of Intelligent GeoInformation Processing(No.KLIGIP-2021B01,KLIGIP-2018B02).
文摘Researchers utilize information from the geoscience literature to deduce the regional or global geological evolution.Traditionally this process has relied on the labor of researchers.As the number of papers continues to increase,acquiring domain-specific knowledge becomes a heavy burden.Knowledge Graph(KG)is proposed as a new knowledge representation technology to change this situation.However,the super relation is not considered in the previous KG,which bridges the geological phenomenon(fact)and its precondition(condition).For instance,in the statement(“the late Archean was a crucial transition period in the history of global geodynamics”),the condition statement(“crucial transition for global geodynamics”)works as the complementary fact statement(“the late Archean was a crucial transition period”),which defines the scale of crucial transition accurately in the late Archean.In this study,fact-condition statement extraction is introduced to construct a geological knowledge graph.A rule-based multi-input multi-output model(R-MIMO)is proposed for information extraction.In the R-MIMO,fact-condition statements and their super relation are considered and extracted for the first time.To verify its performances,a GeothCF dataset with 1455 fact tuples and 789 condition tuples is constructed.In experiments,the R-MIMO model achieves the best performance by using BERT as encoder and LSTM-d as decoder,achieving F180.24%in tuple extraction and F170.03%in tag prediction task.Furthermore,the geothermic KG with super relation is automatically constructed for the first time by trained R-MIMO,which can provide structured data for further geothermic research.
基金supported by National Natural Science Foundation of China(Grant No.61073046)
文摘Let G be a connected graph with vertex-set V(G)and edge-set E(G).A subset F of E(G)is an s-restricted edge-cut of G if G-F is disconnected and every component of G-F has at least s vertices.Letλs(G)be the minimum size of all s-restricted edge-cuts of G andξs(G)=min{|[X,V(G)\X]|:|X|=s,G[X]is connected},where[X,V(G)\X]is the set of edges with exactly one end in X.A graph G with an s-restricted edge-cut is called super s-restricted edge-connected,in short super-λs,ifλs(G)=ξs(G)and every minimum s-restricted edge-cut of G isolates one component G[X]with|X|=s.It is proved in this paper that a connected vertex-transitive graph G with degree k>5 and girth g>5 is super-λs for any positive integer s with s 2g or s 10 if k=g=6.
基金the Key Project of the Ministry of Education of China (205073)Research Fund for Doctorial Program of Higher Education (No.20060255006)
文摘The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, the graph Kuratowski-Mosco convergence and D-convergence of fuzzy (super) pramart and quasi-martingale are studied.
