Injective edge chromatic index of generalized Petersen graph P(ck,k)
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Published:2022-12-31
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Volume:
Page:
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ISSN:1793-8309
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Container-title:Discrete Mathematics, Algorithms and Applications
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language:en
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Short-container-title:Discrete Math. Algorithm. Appl.
Author:
Hu Xiaolan1ORCID,
Legass Belayneh-Mengistu1
Affiliation:
1. School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, P. O. Box 71010, Wuhan 430079, P. R. China
Abstract
An injective [Formula: see text]-edge coloring of a graph [Formula: see text] is a [Formula: see text]-edge coloring [Formula: see text] of [Formula: see text] such that [Formula: see text] for any three consecutive edges [Formula: see text] and [Formula: see text] of a path or a 3-cycle. The injective edge chromatic index of [Formula: see text], denoted by [Formula: see text], is the minimum [Formula: see text] such that [Formula: see text] has an injective [Formula: see text]-edge coloring. Li and Chen determined the injective edge chromatic index of the generalized Petersen graph [Formula: see text] for [Formula: see text]. In this paper, we consider the injective edge coloring of the generalized Petersen graph [Formula: see text] and show that [Formula: see text] for [Formula: see text].
Funder
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics