A Kind Of Conditional Connectivity Of Cayley Graphs Generated By 2-Trees

For a connected graph G = (V(G), E(G)), a subset F subset of V(G) is called an R-k-vertex-cut if G - F is disconnected and each vertex u is an element of V(G) - F has at least k neighbors in G - F. The cardinality of a minimum R-k-vertex-cut of G is the R-k-vertex-connectivity and is denoted by k(k) (G). The conditional 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 2-trees T-2,(n), which are denoted by KTn, and show that k(1)(KTn) = 4n - 8 for n >= 4; k(2) (KTn) = 8n - 22 for n >= 6.