A k-regular spanning subgraph of graph G is called a k-factor of G. Graph G is called a k-deleted graph if G-e has a k-factor for each edge e. A graph G=(X,Y) with bipartition (X,Y) is called a bipartite graph if ever...A k-regular spanning subgraph of graph G is called a k-factor of G. Graph G is called a k-deleted graph if G-e has a k-factor for each edge e. A graph G=(X,Y) with bipartition (X,Y) is called a bipartite graph if every edge of G has one endpoint in X and the other in Y.It is proved that a bipartite graph G=(X,Y) with X=Y is a k-deleted graph if and only if kS≤r 1+2r 2+...+k(r k+...+r Δ)-ε(S) for all SX. Using this result we give a sufficient neighborhood condition for a bipartite to be a k-deleted graph.展开更多
Let Γ be a connected regular bipartite graph of order 18 p, where p is a prime. Assume that Γ admits a group acting primitively on one of the bipartition subsets of Γ. Then, in this paper, it is shown that eitherΓ...Let Γ be a connected regular bipartite graph of order 18 p, where p is a prime. Assume that Γ admits a group acting primitively on one of the bipartition subsets of Γ. Then, in this paper, it is shown that eitherΓ is arc-transitive, or Γ is isomorphic to one of 17 semisymmetric graphs which are constructed from primitive groups of degree 9p.展开更多
文摘A k-regular spanning subgraph of graph G is called a k-factor of G. Graph G is called a k-deleted graph if G-e has a k-factor for each edge e. A graph G=(X,Y) with bipartition (X,Y) is called a bipartite graph if every edge of G has one endpoint in X and the other in Y.It is proved that a bipartite graph G=(X,Y) with X=Y is a k-deleted graph if and only if kS≤r 1+2r 2+...+k(r k+...+r Δ)-ε(S) for all SX. Using this result we give a sufficient neighborhood condition for a bipartite to be a k-deleted graph.
基金supported by National Natural Science Foundation of China(Grant Nos.11271267 and 11371204)
文摘Let Γ be a connected regular bipartite graph of order 18 p, where p is a prime. Assume that Γ admits a group acting primitively on one of the bipartition subsets of Γ. Then, in this paper, it is shown that eitherΓ is arc-transitive, or Γ is isomorphic to one of 17 semisymmetric graphs which are constructed from primitive groups of degree 9p.
