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Toughness of the corona of two graphs

 

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Author: Moreno Casablanca, Rocío
Diánez Martínez, Ana Rosa
García Vázquez, Pedro
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2011
Published in: International Journal of Computer Mathematics, 88 (13), 2697-2706.
Document type: Article
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.
Cite: Moreno Casablanca, R., Diánez Martínez, A.R. y García Vázquez, P. (2011). Toughness of the corona of two graphs. International Journal of Computer Mathematics, 88 (13), 2697-2706.
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URI: https://hdl.handle.net/11441/69650

DOI: 10.1080/00207160.2011.564277

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