Strong Edge Coloring of Generalized Petersen Graphs

Ming Chen, Lianying Miao and Shan Zhou
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Ming Chen: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
Lianying Miao: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
Shan Zhou: School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

Mathematics, 2020, vol. 8, issue 8, 1-12

Abstract: A strong edge coloring of a graph G is a proper edge coloring such that every color class is an induced matching. In 2018, Yang and Wu proposed a conjecture that every generalized Petersen graph P ( n , k ) with k ≥ 4 and n > 2 k can be strong edge colored with (at most) seven colors. Although the generalized Petersen graph P ( n , k ) is a kind of special graph, the strong chromatic index of P ( n , k ) is still unknown. In this paper, we support the conjecture by showing that the strong chromatic index of every generalized Petersen graph P ( n , k ) with k ≥ 4 and n > 2 k is at most 9.

Keywords: strong edge coloring; generalized Petersen graphs; partition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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