Rainbow Domination in Cartesian Product of Paths and Cycles

IF 0.6 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

International Journal of Foundations of Computer Science Pub Date : 2023-11-11 DOI:10.1142/s0129054123500272

Hong Gao, Yunlei Zhang, Yuqi Wang, Yuanyuan Guo, Xing Liu, Renbang Liu, Changqing Xi, Yuansheng Yang

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引用次数: 0

Abstract

Let [Formula: see text] be a graph and [Formula: see text] be an integer representing [Formula: see text] colors. There is a function [Formula: see text] from [Formula: see text] to the power set of [Formula: see text] colors satisfying every vertex [Formula: see text] assigned [Formula: see text] under [Formula: see text] in its neighborhood has all the colors, then [Formula: see text] is called a [Formula: see text]-rainbow dominating function ([Formula: see text]RDF) on [Formula: see text]. The weight of [Formula: see text] is the sum of the number of colors on each vertex all over the graph. The [Formula: see text]-rainbow domination number of [Formula: see text] is the minimum weight of [Formula: see text]RDFs on [Formula: see text], denoted by [Formula: see text]. The aim of this paper is to investigate the [Formula: see text]-rainbow ([Formula: see text]) domination number of the Cartesian product of paths [Formula: see text] and the Cartesian product of paths and cycles [Formula: see text]. For [Formula: see text], we determine the value [Formula: see text] and present [Formula: see text] for [Formula: see text]. For [Formula: see text], we determine the values of [Formula: see text] for [Formula: see text] or [Formula: see text] and [Formula: see text] for [Formula: see text] or [Formula: see text].

查看原文本刊更多论文

路径与循环笛卡尔积中的彩虹支配

设[公式:见文本]为图形，[公式:见文本]为表示[公式:见文本]颜色的整数。有一个函数[Formula: see text]从[Formula: see text]到[Formula: see text]颜色的幂集满足在[Formula: see text]下分配的[Formula: see text]的每个顶点[Formula: see text]在它的邻域中具有所有的颜色，那么[Formula: see text]就被称为[Formula: see text]上的[Formula: see text]-彩虹支配函数([Formula: see text]RDF)。[公式:见文本]的权重是图形上每个顶点的颜色数量之和。[公式:见文]的[公式:见文]-彩虹支配数是[公式:见文]上[公式:见文]rdf的最小权值，用[公式:见文]表示。本文的目的是研究路径的笛卡尔积[公式:见文]和路径与循环的笛卡尔积[公式:见文]的[公式:见文]-彩虹([公式:见文])的支配数。对于[Formula: see text]，我们确定值[Formula: see text]，并为[Formula: see text]呈现[Formula: see text]。对于[公式:见文本]，我们为[公式:见文本]或[公式:见文本]确定[公式:见文本]的值，为[公式:见文本]或[公式:见文本]确定[公式:见文本]的值。

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

International Journal of Foundations of Computer Science 工程技术-计算机：理论方法

CiteScore

1.60

自引率

12.50%

发文量

审稿时长

3 months

期刊介绍： The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include: - Algebraic theory of computing and formal systems - Algorithm and system implementation issues - Approximation, probabilistic, and randomized algorithms - Automata and formal languages - Automated deduction - Combinatorics and graph theory - Complexity theory - Computational biology and bioinformatics - Cryptography - Database theory - Data structures - Design and analysis of algorithms - DNA computing - Foundations of computer security - Foundations of high-performance computing