The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs

Abstract

Let G = (V, E) be a graph. The double vertex graph F 2 (G) of G is the graph whose vertex set consists of all 2-subsets of V (G) such that two vertices are adjacent in F 2 (G) if their symmetric difference is a pair of adjacent vertices in G. The super-connectivity of a connected graph is the minimum number of vertices whose removal results in a disconnected graph without an isolated vertex. In this paper, we determine the super-connectivity of the double vertex graph of the complete bipartite graph K m,n for m ≥ 4 where n ≥ m + 2.