On the Total Domination Number of Cartesian Products of Graphs

被引：0

作者：

Michael A. Henning

Douglas F. Rall

机构：

[1] University of KwaZulu-Natal,School of Mathematics, Statistics, & Information Technology

[2] Furman University,Department of Mathemtics

来源：

Graphs and Combinatorics | 2005年 / 21卷

关键词：

Graph products; Total domination; Vizing’s conjecture;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The most famous open problem involving domination in graphs is Vizing’s conjecture which states the domination number of the Cartesian product of any two graphs is at least as large as the product of their domination numbers. In this paper, we investigate a similar problem for total domination. In particular, we prove that the product of the total domination numbers of any nontrivial tree and any graph without isolated vertices is at most twice the total domination number of their Cartesian product, and we characterize the extremal graphs.

引用

页码：63 / 69

页数：6

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