Title: On Chromaticity of Circulant Graph
Authors: Hanan Hayder Mohammed, Esraa Kareem Kadhim
Volume: 8
Issue: 8
Pages: 140-143
Publication Date: 2024/08/28
Abstract:
Coloring graphs is a fundamental problem that arose during the attempt to resolve the four-color theorem. The main focus lies in finding the minimum number of colors required for a proper graph coloring. Additionally, there is an interest in determining the total count of distinct proper colorings achievable with a specific number of colors on a graph. These values can be computed using the Chromatic Polynomial, a specialized function linked to each graph. Graphs G and H are considered chromatically equivalent if they have the same chromatic polynomial. A graph G is chromatically unique if it is isomorphic to any graph H that is chromatically equivalent to G. The exploration of chromatically equivalent and chromatically unique problems is known as chromaticity. This paper explores the chromaticity of circulant graph, focusing on their chromatic equivalence and uniqueness.