Gap vertex-distinguishing edge colorings of graphs

• Published in: Discrete mathematics Vol. 312; no. 20; pp. 3011 - 3025
• Main Authors: Tahraoui, M.A., Duchêne, E., Kheddouci, H.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 28.10.2012; Elsevier
• Subjects: Coloring; Computer Science; Edge coloring; Gap vertex-distinguishing edge coloring; Graphs; Labels; Marking; Mathematical analysis; Vertex labeling; Gap vertex-distinguishing edge coloring; Vertex labeling; Edge coloring
• ISSN: 0012-365X; 1872-681X
• DOI: 10.1016/j.disc.2012.06.019

In this paper, we study a new coloring parameter of graphs called the gap vertex-distinguishing edge coloring. It consists in an 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 colors required for a gap vertex-distinguishing edge coloring of G is called the gap chromatic number of G and is denoted by gap(G). We here study the gap chromatic number for a large set of graphs G of order n and prove that gap(G)∈{n−1,n,n+1}.