A Kind Of Conditional Vertex Connectivity Of Cayley Graphs Generated By Wheel Graphs. (13th November 2019) - Luo, Zuwen; Xu, Liqiong
Abstract: Let G=(V(G), E(G)) be a connected graph. A subset T V(G) is called an R^k -vertex-cut, if G-T is disconnected and each vertex in V(G)-T has at least k neighbors in G-T . The cardinality of a minimum R^k -vertex-cut is the R^k -vertex-connectivity of G and is denoted by κ ^k(G) . R^k -vertex-connectivity is a new measure to study the fault tolerance of network structures beyond connectivity. In this paper, we study R^1 -vertex-connectivity and R^2 -vertex-connectivity of Cayley graphs generated by wheel graphs, which are denoted by AW_n, and show that κ ^1(AW_n)=4n-7 for n≥ 6 ; κ ^2(AW_n)=6n-12 for n≥ 6 .