On a b-chromatic Sum of a Myceilskian of Paths

Authors

  • Wipawee Tangjai Department of Mathematics, Mahasarakham University, 44150, Thailand
  • Panuponng Vichitkunakorn Division of Computational Science, Faculty of Science, Prince of Songkla University, Songkla 90110, Thailand
  • Sittichai Chaiyakhot Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
  • Rawit Sinthuket Department of Mathematics, Faculty of Science, Mahasarakham University, Maha 251 Sarakham 44150, Thailand

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6188

Keywords:

b-coloring, b-chromatic number, b-dominating, b-chromatic sum, path, Mycielskian

Abstract

A b-coloring of a graph G is a proper coloring such that there exists a vertex in each color class that is adjacent to at least one vertex in other color classes. The b-chromatic number of a graph G, denoted by φ(G), is the largest integer k such that G has b-coloring with k colors. The b-chromatic sum of  graph G, denoted by φ′(G), is defined as the minimum sum of the colors c(v) of v for all v ∈ V where c is a b-coloring with colors 1, 2, . . . , φ(G). In the work, we improve the bounds on the b-chromatic sum given by Lisna and Sunitha [4]. We give the b-chromatic sum of the Mycielskian of a path μ(Pn) when n = 7, 9 and n ≥ 16. For the case 10 ≤ n ≤ 15, we give bounds on φ′(μ(Pn)).

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Discrete Mathematics

License

Copyright (c) 2025 Wipawee Tangjai, Panuponng Vichitkunakorn, Sittichai Chaiyakhot, Rawit Sinthuket

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How to Cite

On a b-chromatic Sum of a Myceilskian of Paths. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6188. https://doi.org/10.29020/nybg.ejpam.v18i3.6188