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Article Dans Une Revue Discrete Mathematics Letters Année : 2023

The b_q-coloring of graphs

Résumé

In this article we introduce a new graph coloring called the b_q-coloring. A b_q-coloring of a graph G is a proper vertex coloring of G with k colors such that every color class c admits a set of vertices S, of size at most q, such that every color except c appears in the neighborhood of S. The aim of this coloring is to generalize the domination constraint given in the b-coloring of a graph where every color admits only one dominating vertex (adjacent to every other color). The largest positive integer k for which a graph has a b_q-coloring using k colors is the b_q-chromatic number. We present some classes of graphs for which the b_q-chromatic number has maximum value and we give exact values of this parameter for paths and cycles. We also present some bounds for Cartesian products of graphs.

Dates et versions

hal-04315094 , version 1 (30-11-2023)

Identifiants

Citer

Brice Effantin. The b_q-coloring of graphs. Discrete Mathematics Letters, 2023, 12, pp.173-180. ⟨10.47443/dml.2023.098⟩. ⟨hal-04315094⟩
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