Domination number of Cartesian product through space projections

被引：0
作者：
Tout, Omar [1 ]
机构：
[1] Sultan Qaboos Univ, Coll Sci, Dept Math, POB 36, Al Khoud 123, Oman
来源：
DISCRETE MATHEMATICS LETTERS | 2024年 / 13卷
关键词：
Cartesian product; domination number; Vizing's conjecture; Clark-Suen bound;
D O I：
10.47443/dml.2024.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In 1968, Vizing conjectured that for every pair of graphs X and Y, the inequality gamma(X square Y) > gamma(X)gamma(Y) holds, where gamma stands for the domination number and X square Y is the Cartesian product of X and Y. In a breakthrough result, Clark and Suen [Electron. J. Combin. 7 (2000) #N4] proved that gamma(X square Y) > 1/2 gamma(X)gamma(Y). In this paper, a lower bound for gamma(X square Y square Z) is obtained using projections in the space. It is shown how the obtained bound implies the mentioned result of Clark and Suen.
引用
收藏
页码：95 / 99
页数：5
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