路径笛卡尔积的双总支配数

IF 1.8 3区 数学 Q1 MATHEMATICS
Linyu Li, Jun Yue, Xia Zhang
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引用次数: 0

摘要

如果$ G $中的每个顶点在$ S $中至少有两个相邻顶点,则图$ G $的顶点集$ S $称为双共支配集。$ G $的双总支配数$ \gamma_{\times 2, t}(G) $是$ G $中所有双总支配集的最小基数。设$ G \square H $表示图$ G $和$ H $的笛卡尔积。本文讨论了路径笛卡尔积的双总支配数。我们确定了$ i = 2, 3 $的$ \gamma_{\times 2, t}(P_i\square P_n) $值,并给出了$ i \geq 4 $的$ \gamma_{\times 2, t}(P_i\square P_n) $的下界和上界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Double total domination number of Cartesian product of paths
A vertex set $ S $ of a graph $ G $ is called a double total dominating set if every vertex in $ G $ has at least two adjacent vertices in $ S $. The double total domination number $ \gamma_{\times 2, t}(G) $ of $ G $ is the minimum cardinality over all the double total dominating sets in $ G $. Let $ G \square H $ denote the Cartesian product of graphs $ G $ and $ H $. In this paper, the double total domination number of Cartesian product of paths is discussed. We determine the values of $ \gamma_{\times 2, t}(P_i\square P_n) $ for $ i = 2, 3 $, and give lower and upper bounds of $ \gamma_{\times 2, t}(P_i\square P_n) $ for $ i \geq 4 $.
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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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