Edge vulnerability parameters of bisplit graphs

  • Authors:

  • Metrose Metsidik;Elkin Vumar

  • Affiliations:

  • College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, PR China;College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, PR China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2008

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Abstract

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 @d(G). We prove that its edge-connectivity is @d(G), and if |Z|=|Y|=32@d(G), then its edge-toughness is min{@d(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|