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Edge vulnerability parameters of bisplit graphs

✍ Scribed by Metrose Metsidik; Elkin Vumar

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 260 KB
Volume: 56
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2008.04.015

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✦ Synopsis

A graph is called bisplit if its vertex set can be partitioned into three stable sets I, Y and Z such that Y ∪ 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). We prove that its edge-connectivity is δ(G),

Examples are given to show that the condition cannot be dropped out. Moreover, it is shown that if |Y ∪ Z | < 2δ(G), then the edge-integrity of G equals |V (G)|.

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