Total Dominator Edge Chromatic Number of Graphs

被引：0

作者：

Li, Minhui ^{[1
]}

Zhang, Shumin ^{[2
]}

Wang, Caiyun ^{[1
]}

Ye, Chengfu ^{[2
]}

机构：

[1] Master candidate of the School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai,810008, China

[2] Professor of the School of Mathematics and Statistics, Academy of Plateau Science and Sustainability, People’s Government of Qinghai Province and Beijing Normal University, Qinghai Normal University, Xining, Qinghai,810008, China

来源：

IAENG International Journal of Applied Mathematics | 2021年 / 51卷 / 04期

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摘要：

Let G be a simple graph with no isolated edge. A total dominator edge coloring (TDEC) of a graph G is a proper edge coloring such that each edge of G is adjacent to every edge of some (other) color class. The total dominator edge chromatic number (TDEC-number) of G is the minimum number of color classes among all total dominator edge colorings of G, denoted by (Formula presented)(G)· The stability number of TDEC-number of G is the minimum number of vertices whose removal changes the value of (Formula presented) (G) and remaining graph is connected· The bondage number of TDEC-number of G is the minimum number of edges whose removal changes the value of (Formula presented) (G). In this paper, we establish the lower and upper bounds of the TDEC-number of a graph G, obtain the TDEC-number and the stability and bondage numbers of some graphs· © 2021. All Rights Reserved.

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