Edge vulnerability parameters of bisplit graphs

A graph is called bisplitbisplit if its vertex set can be partitioned into three stable sets I,YI,Y and ZZ such that Y∪ZY∪Z induces a complete bipartite graph (a biclique  ). In this paper, we investigate the edge vulnerability parameters of bisplit graphs. Let G=(Y∪Z,I,E) be a noncomplete connected bisplit graph with minimum vertex degree δ(G)δ(G). We prove that its edge-connectivity is δ(G)δ(G), and if |Z|≥|Y|≥32δ(G), then its edge-toughness is min{δ(G),|E(G)||V(G)|−1}. Examples are given to show that the condition cannot be dropped out. Moreover, it is shown that if |Y∪Z|<2δ(G)|Y∪Z|<2δ(G), then the edge-integrity of GG equals |V(G)||V(G)|.