The super-connectivity of graphs with two orbits  

作　　者：CHEN Lai-huan MENG Ji-xiang YANG Wei-hua LIU Feng-xia 

机构地区：[1]College of Mathematics and Information Sciences,Henan University of Economics and Law,Zhengzhou 450046,China [2]College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China [3]Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2024年第4期571-583,共13页高校应用数学学报（英文版）（B辑）

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).

摘　　要：A graph G is said to be super-connected or simply super-κ, 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-κ. For 2-edge-orbit graphs,we give a sufficient condition for connected 2-edge-orbit graphs to be super-κ. 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 ≤ 6and girth g(G) ≥ 8, then G is super-connected.

关 键 词：super-connectivity superatom edge orbit 

分 类 号：O157.5[理学—数学]