Captive domination in graphs

被引：20

作者：

Al-Harere, Manal N. ^{[1
]}

Omran, Ahmed A. ^{[2
]}

Breesam, Athraa T. ^{[1
]}

机构：

[1] Univ Technol Baghdad, Dept Appl Sci, Baghdad, Iraq

[2] Univ Babylon, Coll Educ Pure Sci, Dept Math, Babylon, Iraq

来源：

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2020年 / 12卷 / 06期

关键词：

Dominating set; domination number; total domination number; captive domination number;

D O I：

10.1142/S1793830920500767

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new definition of graph domination called "Captive Domination" is introduced. The proper subset of the vertices of a graph G is a captive dominating set if it is a total dominating set and each vertex in this set dominates at least one vertex which doesn't belong to the dominating set. The inverse captive domination is also introduced. The lower and upper bounds for the number of edges of the graph are presented by using the captive domination number. Moreover, the lower and upper bounds for the captive domination number are found by using the number of vertices. The condition when the total domination and captive domination number are equal to two is discussed and obtained results. The captive domination in complement graphs is discussed. Finally, the captive dominating set of paths and cycles are determined.

引用

页数：9

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