On rainbow domination of generalized Petersen graphs P(ck,k)

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-08-08 DOI:10.1016/j.dam.2024.07.052

引用次数: 0

Abstract

The structure of minimal weight rainbow domination functions of cubic graphs are studied. Based on general observations for cubic graphs, generalized Petersen graphs $P (c k, k)$ are characterized whose 4- and 5-rainbow domination numbers equal the general lower bounds. As $t$ -rainbow domination of cubic graphs for $t \geq 6$ is trivial, characterizations of such generalized Petersen graphs $P (c k, k)$ are known for all $t$ -rainbow domination numbers. In addition, new upper bounds for 4- and 5-rainbow domination numbers that are valid for all $P (c k, k)$ are provided.

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论广义彼得森图 P(ck,k) 的彩虹支配作用

研究了立方图的最小权虹支配函数的结构。根据对立方图的一般观察，研究了广义彼得森图 P(ck,k)的特征，其 4- 和 5- 彩虹支配数等于一般下限。由于立方图的 t-rainbow 支配数 t≥6 是微不足道的，因此已知所有 t-rainbow 支配数的广义彼得森图 P(ck,k) 的特征。此外，还提供了对所有 P(ck,k) 都有效的 4- 和 5- 彩虹支配数的新上限。

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.