The authors investigate locally order 18p. It is shown that such a graph the Gray graph and the Tutte 12-cage. primitive bipartite regular connected graphs of is either arc-transitive or isomorphic to one of
As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,...As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,where 1 ≤ m ≤ n,the mcompetition index( generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y,there exist m distinct vertices v_1,v_2,…,v_m such that there exist walks of length k from x to v_i and from y to v_i for 1 ≤ i ≤ m. By analyzing the structure of θ-graphs( theta graphs) and using enumeration investigation methods,the mcompetition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized.展开更多
The exponent of a primitive digraph has been generalized in [2].In this paper we obtain new parameters on generalized exponent of primitive simple graphs (symmetric primitive (0,1)matrices with zero trace) completely.
Let G_(n)([-1]^(i))denote the set of all connected graphs on n vertices having distance eigenvalue-1 of multiplicity i.By using the distribution of the third largest distance eigenvalue and the second least distance e...Let G_(n)([-1]^(i))denote the set of all connected graphs on n vertices having distance eigenvalue-1 of multiplicity i.By using the distribution of the third largest distance eigenvalue and the second least distance eigenvalue of a connected graph,in this paper we completely characterize the graphs in G_(n)([-1]^(i)),where i=n-1,n-2,n-3 or n-4.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11271267,11371204)
文摘The authors investigate locally order 18p. It is shown that such a graph the Gray graph and the Tutte 12-cage. primitive bipartite regular connected graphs of is either arc-transitive or isomorphic to one of
基金Shanxi Scholarship Council of China(No.2012-070)Foundation of North University of China(No.2013-12-1)
文摘As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,where 1 ≤ m ≤ n,the mcompetition index( generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y,there exist m distinct vertices v_1,v_2,…,v_m such that there exist walks of length k from x to v_i and from y to v_i for 1 ≤ i ≤ m. By analyzing the structure of θ-graphs( theta graphs) and using enumeration investigation methods,the mcompetition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized.
文摘The exponent of a primitive digraph has been generalized in [2].In this paper we obtain new parameters on generalized exponent of primitive simple graphs (symmetric primitive (0,1)matrices with zero trace) completely.
基金This work is supported by the National Natural Science Foundation of China(12061074).
文摘Let G_(n)([-1]^(i))denote the set of all connected graphs on n vertices having distance eigenvalue-1 of multiplicity i.By using the distribution of the third largest distance eigenvalue and the second least distance eigenvalue of a connected graph,in this paper we completely characterize the graphs in G_(n)([-1]^(i)),where i=n-1,n-2,n-3 or n-4.
