Research ArticleNo Access

The characterization of lucky edge coloring in graphs

A. Anantayasethi

https://orcid.org/0000-0002-3842-9959

Algebra and Applications Research Unit, Mahasarakham University, Mahasarakham 44150, Thailand

E-mail Address: ananya.a@msu.ac.th

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J. Koppitz

Institute of Mathematics and Informatics, Bulgaria Academy of Sciences 14476 Sofia, Bulgaria

E-mail Address: koppitz@math.bas.bg

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S. Worawiset

Mathematics Department, Faculty of Science, Khon Kaen University, Khon Kaen 40000, Thailand

E-mail Address: wsomnu@kku.ac.th

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, and

K. Saengsura

Algebra and Applications Research Unit, Mahasarakham University, Mahasarakham 44150, Thailand

E-mail Address: kittisak.s@msu.ac.th

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https://doi.org/10.1142/S1793557123501280Cited by:0 (Source: Crossref)

Abstract

The lucky edge coloring of graph $G$ is a proper edge coloring which is induced by a vertex coloring such that each edge is labeled by the sum of its vertices. The least integer $k$ for which $G$ has a lucky edge coloring in the set ${1, 2, \dots, k}$ is called lucky number, denoted by $η (G)$ . The lucky numbers were already calculated for a large number of graphs, but not yet for trees. In this paper, we provide the characterization of lucky edge coloring and calculate the lucky number for graphs which can be regarded as complete $m$ -ary trees.

Communicated by I. Dimitrova

Keywords:

AMSC: 05C05, 05C07, 05C15, 05C30

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