Complexity of 2-Rainbow Total Domination Problem

IF 1 3区数学 Q1 MATHEMATICS

Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-08-08 DOI:10.1007/s40840-024-01747-8

Tadeja Kraner Šumenjak, Aleksandra Tepeh

引用次数: 0

Abstract

In this paper, we extend the findings of recent studies on k-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a 2-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the k-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the k-rainbow total domination number of the corona product \(G*H\), provided that H has enough vertices.

Abstract Image

查看原文本刊更多论文

双彩虹全面统治问题的复杂性

在本文中，我们将重点放在 k-rainbow 总支配的计算复杂性方面，从而扩展了近期关于 k-rainbow 总支配的研究成果。我们证明，判断一个图是否具有给定权重的 2-rainbow 总支配函数的问题是 NP-完全的。即使局限于平面图，这一复杂性结果也是成立的。同时，我们还建立了有根积图的 k-rainbow 总支配数的严格边界。此外，我们还得到了冠积 \(G*H\)的 k-rainbow 总支配数的封闭公式，前提是 H 有足够多的顶点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.