A characterization of graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-08-22 DOI:10.1016/j.dam.2024.08.008

Teresa W. Haynes , Michael A. Henning

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引用次数: 0

Abstract

A set $S$ of vertices in a graph $G$ is a dominating set if every vertex not in $S$ is adjacent to a vertex in $S$ . If, in addition, $S$ is an independent set, then $S$ is an independent dominating set, while if every vertex of the dominating set $S$ is adjacent to a vertex in $S$ , then $S$ is a total dominating set of $G$ . A fundamental problem in domination theory in graphs is to determine which graphs have the property that their vertex set can be partitioned into two types of dominating sets. In particular, we are interested in graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set. In this paper, we solve this problem by providing a constructive characterization of such graphs. We show that all such graphs can be constructed starting from two base graphs and applying a sequence of eleven operations.

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顶点集可划分为总支配集和独立支配集的图的特征描述

如果不在 S 中的每个顶点都与 S 中的顶点相邻，那么图 G 中的顶点集 S 就是支配集。此外，如果 S 是独立集，那么 S 就是独立支配集；如果支配集 S 中的每个顶点都与 S 中的顶点相邻，那么 S 就是 G 的总支配集。特别是，我们对顶点集可划分为总支配集和独立支配集的图感兴趣。在本文中，我们通过提供此类图的构造性特征来解决这个问题。我们证明，所有此类图都可以从两个基图开始，应用 11 个操作序列来构造。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.