#### Filter Results:

#### Publication Year

2000

2016

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

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)

Let G be a graph on vertices v 1 , v 2 ,. .. , v n. The b-chromatic number of G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i ≤ k, has at least one representant x i adjacent to a vertex of every color j, 1 ≤ j = i ≤ k. In this paper, we give the… (More)

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion… (More)

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)

A b-coloring of a graph is a proper coloring where each color admits at least one node (called dominating node) adjacent to every other used color. Such a coloring gives a partitioning of the graph in clusters for which every cluster has a clusterhead (the dominating node) adjacent to each other cluster. Such a decomposition is very interesting for large… (More)