Opuscula Math. 41, no. 2 (2021), 245-257

Opuscula Mathematica

Introduction to dominated edge chromatic number of a graph

Mohammad R. Piri
Saeid Alikhani

Abstract. We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph \(G\), is a proper edge coloring of \(G\) such that each color class is dominated by at least one edge of \(G\). The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by \(\chi_{dom}^{\prime}(G)\). We obtain some properties of \(\chi_{dom}^{\prime}(G)\) and compute it for specific graphs. Also examine the effects on \(\chi_{dom}^{\prime}(G)\), when \(G\) is modified by operations on vertex and edge of \(G\). Finally, we consider the \(k\)-subdivision of \(G\) and study the dominated edge chromatic number of these kind of graphs.

Keywords: dominated edge chromatic number, subdivision, operation, corona.

Mathematics Subject Classification: 05C25.

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  • Mohammad R. Piri
  • Yazd University, Department of Mathematics, 89195-741, Yazd, Iran
  • Communicated by Dalibor Fronček.
  • Received: 2020-03-19.
  • Revised: 2020-12-24.
  • Accepted: 2021-02-04.
  • Published online: 2021-03-17.
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Cite this article as:
Mohammad R. Piri, Saeid Alikhani, Introduction to dominated edge chromatic number of a graph, Opuscula Math. 41, no. 2 (2021), 245-257, https://doi.org/10.7494/OpMath.2021.41.2.245

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