Edge vulnerability parameters of split graphs

A graph is called a split graph if its vertex set can be partitioned into a clique and an independent set. In this work, we investigate three vulnerability parameters of split graphs when edges are removed, i.e., edge-connectivity, edge-toughness and edge-integrity. It is proved that, for a noncomplete connected split graph G, its edge-connectivity is δ (G), and its edge-toughness is min {δ (G), frac(| E (G) |, | V (G) | - 1)}, where δ (G), V (G) and E (G), are the minimum degree, the vertex set and the edge set of G, respectively. Furthermore, we show that the edge-integrity of a noncomplete connected split graph equals its order when its minimum degree is greater than half of the size of its largest clique.