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Article Dans Une Revue International Journal of Computer Mathematics Année : 2011

On the toughness of the corona of two graphs

Rocio M. Casablanca
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Ana Diánez
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Résumé

The toughness of a noncomplete graph $G=(V,E)$ is defined as $\tau(G)=\min\{|S|/\omega(G-S)\}$, where the minimum is taken over all cutsets $S$ of vertices of $G$ and $\omega(G-S)$ 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 $G\circ H$, is the graph obtained by taking one copy of $G$ and $|V(G)|$ copies of $H$, and then joining the $i$th vertex of $G$ to every vertex in the $i$th 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.

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Dates et versions

hal-00710050 , version 1 (20-06-2012)

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Rocio M. Casablanca, Ana Diánez, Pedro García-Vázquez. On the toughness of the corona of two graphs. International Journal of Computer Mathematics, 2011, pp.1. ⟨10.1080/00207160.2011.564277⟩. ⟨hal-00710050⟩

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