Chromatic Polynomial of Intuitionistic Fuzzy Graphs(IFGs) Using α-Levels

Abstract Objective: In graph coloring, determining the chromatic polynomial is exactly finding the number of alternative solutions anywhere graph coloring is applied. In this article, We use α level to compute the chromatic polynomial of the Intuitionistic fuzzy graph. In addition, We convert (α,β) level to α level and define α level graph. Moreover, We compute the chromatic polynomial for the different α level graphs with illustrative examples.Results: (α,β)- level to α-level conversion method is developed, and based on that α level graph is defined. Besides, the different α level graphs are computed with illustrative examples. In addition, certain properties of α- level graphs and their chromatic polynomials are presented. Moreover, the chromatic number, the number of vertices, the number of edges, and the chromatic polynomial of the different α-level graphs are compared.Mathematics Subject Classification: Primary: 05C72, 05C31. Secondary: 03B20, 03E72.