2014/05/25 by Ali Mansouri, Mansouri, Ali, Med Salim Bouhlel +2
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1405.6432
arxiv created 2014/05/25 · openalex publication_date 2014/05/25 · arxiv updated 2014/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, is adjacent to (i - 1) vertices colored with each color j, In this paper we give bounds for the Grundy number of some graphs and Cartesian products of graphs. In particular, we determine an exact value of this parameter for n-dimensional meshes and some n-dimensional toroidal meshes. Finally, we present an algorithm to generate all graphs for a given Grundy number