On Equitable Colorings of Windmill Graphs

Authors

DOI:

https://doi.org/10.37256/cm.5320245130

Keywords:

equitable coloring, equitable chromatic number, equitable chromatic threshold, windmill graphs

Abstract

Let G be an undirected simple graph. Graph coloring is a special case of labeling, and G is said to admit a proper coloring if no two neighbouring vertices of it are given the identical color. The vertices of identical color constitute a color class. A graph is p-colorable if it has a p-coloring. The chromatic number of G, denoted by χ(G), is the minimum p such that G is p-colorable. A graph G is equitably p-colorable if it has a p-coloring and the absolute difference in size between any two distinct color classes is at most 1. The equitable chromatic number of G, denoted by χ=(G), is the minimum p such that G is equitably p-colorable. The equitable chromatic threshold of G, denoted by mceclip3.png, is the minimum p such that G is equitably p-colorable for all p p . A windmill graph Wnm consists of m copies of the complete graph Kn, with every vertex connected to a common vertex. In this paper, we give exact values of χ=(G) and mceclip2.png when G is a windmill graph, bistar windmill graph, cycle windmill graph, and complete windmill graph.

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Published

2024-09-25

How to Cite

1.
P E, A P. On Equitable Colorings of Windmill Graphs. Contemp. Math. [Internet]. 2024 Sep. 25 [cited 2024 Oct. 13];5(3):4064-78. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/5130

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Section

Special Issue: Recent developments in pure and applied mathematics and its applications