Hamamache Kheddouci

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In this paper, we study a new coloring parameter of a graph called the Gap vertex-distinguishing edge coloring. It is a proper edge-coloring of a graph G which induces a vertex distinguishing labeling of G such that the label of each vertex is given by the difference between the highest and the lowest colors of its adjacent edges. The minimum number of(More)
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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)