Toughness of the corona of two graphs

Abstract

The toughness of a non-complete graph G = (V , E) 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. The corona of two graphs G and H , written as G ◦ H , is the graph obtained by taking one copy of G and |V (G)| copies of H , and then joining the ith vertex of G to every vertex in the ith copy of H . In this paper, we investigate the toughness of this kind of graphs and obtain the exact value for the corona of two graphs belonging to some families as paths, cycles, stars, wheels or complete graphs.