On the vulnerability of some families of graphs

Abstract

The toughness of a noncomplete graph G is defined as τ (G) = min{|S|/ω(G − S)}, where the minimum is taken over all cutsets S of vertices of G and ω(G − S) denotes the number of components of the resultant graph G − S by deletion of S. In this paper, we investigate the toughness of the corona of two connected graphs and obtain the exact value for the corona of two graphs belonging to some families as paths, cycles, wheels or complete graphs. We also get an upper and a lower bounds for the toughness of the cartesian product of the complete graph $K_2$ with a predetermined graph G.