Exact values for the Grundy number of some graphs
Ali Mansouri, Mohamed Salim Bouhlel
TL;DR
This paper investigates the Grundy number, a graph coloring parameter, providing bounds, exact values for specific graph classes like meshes, and an algorithm for generating graphs with a given Grundy number.
Contribution
It offers new bounds, exact calculations for n-dimensional meshes, and an algorithm to generate graphs with specified Grundy numbers, advancing understanding of this graph invariant.
Findings
Exact Grundy number for n-dimensional meshes
Bounds for Grundy number of certain graphs
Algorithm for generating graphs with a given Grundy number
Abstract
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
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Graph theory and applications