Distance-2 Self-stabilizing Algorithm for a b-Coloring of Graphs
Résumé
A b-coloring of a graph G is a proper $k$-coloring of G such that for each color $i$, $1 \leq i\leq k$, at least one vertex colored with $i$ is adjacent to every color $j$, with $1\leq j\neq i\leq k$. This kind of coloring is useful to decompose any system into communities, where each community contains a vertex adjacent to all the other communities. This kind of organization can provide improving in many fields, especially in the data clustering. In this paper we propose a new self-stabilizing algorithm for finding a b-coloring of arbitrary undirected connected graphs. Because the characteristics of the b-coloring problem, the proposed self-stabilizing algorithm use a distance-2 knowledge.