Hamamache Kheddouci

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The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex x colored with color i, 1 ≤ i ≤ k, is adjacent to (i − 1) vertices colored with each color j, 1 ≤ j ≤ i − 1. In this paper we give bounds for the Grundy number of some graphs and cartesian products of graphs. In(More)
An i-packing in a graph G is a set of vertices at pairwise distance greater than i. For a nondecreasing sequence of integers S = (s1, s2,. . .), the S-packing chromatic number of a graph G is the least integer k such that there exists a coloring of G into k colors where each set of vertices colored i, i = 1,. .. , k, is an si-packing. This paper describes(More)
Graph coloring is used to characterize some properties of graphs. A b-coloring of a graph G (using colors 1,2,…,k) is a coloring of the vertices of G such that (i) two neighbors have different colors (proper coloring) and (ii) for each color class there exists a dominating vertex which is adjacent to all other k-1 color classes. In this paper, we build on(More)