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On the Equality of the Grundy Numbers of a Graph

Abstract : Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked(affected) this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. Thus the problem of stability of the network ad hoc which corresponds to a problem of allocation of frequency amounts to a problem of allocation of colors in the vertex of graph. we present use a parameter of coloring " the number of Grundy”. The Grundy number of a graph G, denoted by Γ(G), is the largest k such that G has a greedy k-coloring, that is a coloring with colours obtained by applying the greedy algorithm according to some ordering of the vertices of G. In this paper, we study the Grundy number of the lexicographic, Cartesian and direct products of two graphs in terms of the Grundy numbers of these graphs.
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Contributor : Ali Mansouri Connect in order to contact the contributor
Submitted on : Monday, February 9, 2015 - 1:54:48 PM
Last modification on : Tuesday, June 23, 2020 - 12:30:04 PM

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Ali Mansouri, Mohamed Salim Bouhlel. On the Equality of the Grundy Numbers of a Graph. International Journal of Next-Generation Networks, 2013, 5 (4), pp.13. ⟨10.5121/ijngn.2013.5402⟩. ⟨hal-01114420⟩



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