The Dominator Edge Coloring of Graphs. (7th October 2021)

• Record Type: Journal Article
• Authors: Li, Minhui; Zhang, Shumin; Wang, Caiyun; Ye, Chengfu
• Other Names: Imran Muhammad Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-10-07
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/8178992
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Let G be a simple graph. A dominator edge coloring (DE-coloring) of G is a proper edge coloring in which each edge of G is adjacent to every edge of some color class (possibly its own class). The dominator edge chromatic number (DEC-number) of G is the minimum number of color classes among all dominator edge colorings of G, denoted by χ d ′ G . In this paper, we establish the bounds of the DEC-number of a graph, present the DEC-number of special graphs, and study the relationship of the DEC-number between G and the operations of G .