Let G be a graph, and F={F1, F2,…,Fm} and H be a factorization and a subgraph of G, respectively. If H has exactly one edge in common with Fi for all i, 1≤i≤m, then we say that F is orthogonal to H. Let g and f be ...Let G be a graph, and F={F1, F2,…,Fm} and H be a factorization and a subgraph of G, respectively. If H has exactly one edge in common with Fi for all i, 1≤i≤m, then we say that F is orthogonal to H. Let g and f be two integer-valued functions defined on V(G) such that 0≤g(x)≤f(x) for every x∈V(G). In this paper, it is proved that for any given star with m edges of an (mg+m-1, mf-m + 1)-graph G, there exists a (g,f)-factorization of G orthogonal to it.展开更多
Diagnosability of a multiprocessor system is an important study topic. S. L. Peng, C. K. Lin, J. J. M. Tan, and L. H. Hsu [Appl. Math. Comput., 2012, 218（21）： 10406-10412] proposed a new measure for fault diagnosis...Diagnosability of a multiprocessor system is an important study topic. S. L. Peng, C. K. Lin, J. J. M. Tan, and L. H. Hsu [Appl. Math. Comput., 2012, 218（21）： 10406-10412] proposed a new measure for fault diagnosis of the system, which is called the 9-good-neighbor conditional diagnosability that restrains every fault-free node containing at least 9 fault-free neighbors. As a famous topological structure of intereonnection networks, the n-dimensional star graph Sn has many good properties. In this paper, we establish the 9_good-neighbor conditional diagnosability of Sn under the PMC model and MM＊ model.展开更多
Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a st...Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a star set forμin G.The star complement provides a strong link between graph structure and linear algebra.In this paper,the authors characterize the regular graphs with K2,2,s(s≥2)as a star complement for all possible eigenvalues,the maximal graphs with K2,2,s as a star complement for the eigenvalueμ=1,and propose some questions for further research.展开更多
基金the Mathematics Tianyuan Foundation and Doctoral Discipline Foundation
文摘Let G be a graph, and F={F1, F2,…,Fm} and H be a factorization and a subgraph of G, respectively. If H has exactly one edge in common with Fi for all i, 1≤i≤m, then we say that F is orthogonal to H. Let g and f be two integer-valued functions defined on V(G) such that 0≤g(x)≤f(x) for every x∈V(G). In this paper, it is proved that for any given star with m edges of an (mg+m-1, mf-m + 1)-graph G, there exists a (g,f)-factorization of G orthogonal to it.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 61370001）.
文摘Diagnosability of a multiprocessor system is an important study topic. S. L. Peng, C. K. Lin, J. J. M. Tan, and L. H. Hsu [Appl. Math. Comput., 2012, 218（21）： 10406-10412] proposed a new measure for fault diagnosis of the system, which is called the 9-good-neighbor conditional diagnosability that restrains every fault-free node containing at least 9 fault-free neighbors. As a famous topological structure of intereonnection networks, the n-dimensional star graph Sn has many good properties. In this paper, we establish the 9_good-neighbor conditional diagnosability of Sn under the PMC model and MM＊ model.
基金supported by the National Natural Science Foundation of China(No.11971180,12271337)the Guangdong Provincial Natural Science Foundation(No.2019A1515012052)。
文摘Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a star set forμin G.The star complement provides a strong link between graph structure and linear algebra.In this paper,the authors characterize the regular graphs with K2,2,s(s≥2)as a star complement for all possible eigenvalues,the maximal graphs with K2,2,s as a star complement for the eigenvalueμ=1,and propose some questions for further research.
