Some conditional vertex connectivities of complete-transposition graphs

Abstract

A subset F⊂V(G) is called an Rk-vertex-cut if G-F is disconnected and each vertex u∈V(G)-F has at least k neighbors in G-F. The cardinality of a minimum Rk-vertex-cut is the Rk-vertex-connectivity of G and is denoted by κk(G). The conditional connectivity is a measure to study the structure of networks beyond connectivity. Hypercubes form the basic classes of interconnection networks. Complete transposition graphs were introduced to be competitive models of hypercubes. In this paper, we determine the numbers κ1 and κ2 for complete-transposition graphs, κ1(CTn)=n(n-1)-2,κ2(CT4)=16 and κ2(CTn)=2n(n-1)-10 for n⩾5.