Research Article Chromatic Polynomial of Intuitionistic Fuzzy Graphs Using (α, β)- Levels V. N. SrinivasaRao Repalle , Lateram Zawuga Hordofa , and Mamo Abebe Ashebo Department of Mathematics, College of Natural and Computational Sciences, Wollega University, Nekemte, Ethiopia Correspondence should be addressed to V. N. SrinivasaRao Repalle; rvnrepalle@gmail.com Received 1 April 2022; Revised 31 May 2022; Accepted 6 June 2022; Published 28 June 2022 Academic Editor: V. Ravichandran Copyright © 2022 V. N. SrinivasaRao Repalle et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e article describes a new thought on the chromatic polynomial of an intuitionistic fuzzy graph which is illustrated based on (α, β)-level graphs. Besides, the alpha-beta fundamental set of an intuitionistic fuzzy graph is also defined with a vivid description. In addition to that, some characterizations of the chromatic polynomial of an intuitionistic fuzzy graph are specified as well verified. Furthermore, some untouched properties of the (α, β)-level graph are also projected and proved. 1. Introduction Graph coloring has a lot of applications in areas such as wireless radio channel assignment [1], timetable scheduling [2], and job scheduling [3]. Graph coloring is described as vertex coloring, edge coloring, and map coloring. e concept of the chromatic polynomial was introduced as the number of distinct ways of performing map coloring [4]. e chromatic polynomials of many families of graphs have been computed so far [5, 6]. In addition, the computations of the chromatic polynomials of certain graphs using the Mobius inversion theorem were reported by Srinivasa Rao et al. [7]. e fuzzy set theory was introduced by Zadeh [8]. A fuzzy set communicates an element of a given set with a membership value in [0, 1]. e introduction of fuzzy graph theory was given based on the fuzzy set introduced by Kauffman [9]. e traditional fuzzy set cannot be used to completely describe all evidence in the problems where someone wants to know how much nonmembership values. Such a problem got a solution by Atanassov who introduced an intuitionistic fuzzy set (IFS) [10]. IFS is an extension of Zadeh’s set theory and is described by a membership function, a nonmembership function, and a hesitation function [10]. e concept of an intuitionistic fuzzy graph (IFG) was introduced by Atanassov [11]. Atanassov and Shannon developed certain properties of IFGs [12]. And also, Akram and Davvaz discussed more properties of IFGs [13]. Akram et al. presented strong IFGs and intuitionistic fuzzy line graphs [14]. Akram et al. presented an algorithm for computing the sum distance matrix, eccentricity, radius, and diameter of IFG [15]. Electoral systems [16], human cells clustering [17], and water supply systems [18] are some application areas of IFGs. Also, IFG digraph is applied in medical diagnosis, gas pipelines, and decision-making sys- tems [19]. e chromatic polynomials of fuzzy graphs using α-cuts and their algebraic properties were developed by Abebe and Srinivasa Rao Repalle [20]. e coloring of IFG using (α, β)-cuts (levels) was introduced by Mohideen and Rifayathali [21]. Some properties of IFG by (α, β)-levels were presented by Akram [22]. To fill the gap in these articles, the authors aimed to find the chromatic polynomial of IFG using (α, β)-levels, define(α, β)-fundamental set, and discuss more untouched properties of(α, β)-level graphs. is paper presents the chromatic polynomial of an IFG using (α, β)-levels by illustrating it based on (α, β)-level graphs. In addition, it defines the alpha-beta fundamental set of an IFG. Furthermore, it states and proves some properties of the (α, β)-level graph and the chromatic polynomial of IFG. is manuscript is organized as follows: Section 2 is the preliminaries that are essential for understanding the article. Section 3develops some properties of(α, β)-levels of IFGs and Hindawi International Journal of Mathematics and Mathematical Sciences Volume 2022, Article ID 9320700, 7 pages https://doi.org/10.1155/2022/9320700