Edge lifting and total domination in graphs

被引：0
|
作者：
Wyatt J. Desormeaux
Teresa W. Haynes
Michael A. Henning
机构：
[1] University of Johannesburg,Department of Mathematics
[2] East Tennessee State University,Department of Mathematics and Statistics
来源：
Journal of Combinatorial Optimization | 2013年 / 25卷
关键词：
Edge lifting; Edge splitting; Total domination;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let u and v be vertices of a graph G, such that the distance between u and v is two and x is a common neighbor of u and v. We define the edge lift of uv off x as the process of removing edges ux and vx while adding the edge uv to G. In this paper, we investigate the effect that edge lifting has on the total domination number of a graph. Among other results, we show that there are no trees for which every possible edge lift decreases the total domination number and that there are no trees for which every possible edge lift leaves the total domination number unchanged. Trees for which every possible edge lift increases the total domination number are characterized.
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页码：47 / 59
页数：12
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