Let G be a finite group and let S（possibly, contains the identity element） be a subset of G. The Bi-Cayley graph BC（G, S） is a bipartite graph with vertex set G × { 0,1} and edge set {（g, 0） （sg,1） ： g∈...Let G be a finite group and let S（possibly, contains the identity element） be a subset of G. The Bi-Cayley graph BC（G, S） is a bipartite graph with vertex set G × { 0,1} and edge set {（g, 0） （sg,1） ： g∈ G, s ∈ S}. A graph is said to be super-connected ff every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if every minimum vertex cut creates two components, one of which is an isolated vertex. In this paper, super-connected and/or hyper-connected cubic Bi-Cayley graphs are characterized.展开更多
A graph G is said to be super-connected or simply super-k,if each minimum vertex cut of G isolates a vertex.A graph G is said to be a k-vertex-orbit graph if there are k vertex orbits when Aut(G)acts on V(G).A graph G...A graph G is said to be super-connected or simply super-k,if each minimum vertex cut of G isolates a vertex.A graph G is said to be a k-vertex-orbit graph if there are k vertex orbits when Aut(G)acts on V(G).A graph G is said to be a k-edge-orbit graph if there are k edge orbits when Aut(G)acts on edge set E(G).In this paper,we give a necessary and sufficient condition for connected bipartite 2-vertex-orbit graphs to be super-k.For 2-edge-orbit graphs,we give a sufficient condition for connected 2-edge-orbit graphs to be super-k.In addition,we show that if G is a k-regular connected irreducible II-kind 2-edge-orbit graph with k≤6 and girth g(G)≥6,or G is a k-regular connected irreducible III-kind 2-edge-orbit graph with k≤6 and girth g(G)≥8,then G is super-connected.展开更多
文摘Let G be a finite group and let S（possibly, contains the identity element） be a subset of G. The Bi-Cayley graph BC（G, S） is a bipartite graph with vertex set G × { 0,1} and edge set {（g, 0） （sg,1） ： g∈ G, s ∈ S}. A graph is said to be super-connected ff every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if every minimum vertex cut creates two components, one of which is an isolated vertex. In this paper, super-connected and/or hyper-connected cubic Bi-Cayley graphs are characterized.
基金Supported by the National Natural Science Foundation of Xinjiang(2020D04046)the National Natural Science Foundation of Shanxi(20210302123097)the National Natural Science Foundation of China(12371356,11961067).
文摘A graph G is said to be super-connected or simply super-k,if each minimum vertex cut of G isolates a vertex.A graph G is said to be a k-vertex-orbit graph if there are k vertex orbits when Aut(G)acts on V(G).A graph G is said to be a k-edge-orbit graph if there are k edge orbits when Aut(G)acts on edge set E(G).In this paper,we give a necessary and sufficient condition for connected bipartite 2-vertex-orbit graphs to be super-k.For 2-edge-orbit graphs,we give a sufficient condition for connected 2-edge-orbit graphs to be super-k.In addition,we show that if G is a k-regular connected irreducible II-kind 2-edge-orbit graph with k≤6 and girth g(G)≥6,or G is a k-regular connected irreducible III-kind 2-edge-orbit graph with k≤6 and girth g(G)≥8,then G is super-connected.
基金Project 10261005 supported by National Natural Science Foundation of China and project 20001301 supported by Natural Science Foundation of Inner Mongolia.
