Affiliation:
1. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran
Abstract
Let [Formula: see text] be a finite and simple graph with vertex set [Formula: see text]. Let [Formula: see text] be a function that assigns label from the set [Formula: see text] to the vertices of a graph [Formula: see text]. For a vertex [Formula: see text], the active neighborhood of [Formula: see text], denoted by [Formula: see text], is the set of vertices [Formula: see text] such that [Formula: see text]. A quadruple Roman dominating function (QRDF) is a function [Formula: see text] satisfying the condition that for any vertex [Formula: see text] with [Formula: see text]. The weight of a QRDF is [Formula: see text]. The quadruple Roman domination number [Formula: see text] of [Formula: see text] is the minimum weight of a QRDF on [Formula: see text]. In this paper, we investigate the properties of the quadruple Roman domination number of graphs, present bounds on [Formula: see text] and give exact values for some graph families. In addition, complexity results are also obtained.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics
Cited by
7 articles.
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1. Further Results on the [k]-Roman Domination in Graphs;Bulletin of the Iranian Mathematical Society;2024-03-27
2. On [
k
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3. New bounds on the outer-independent total double Roman domination number;Discrete Mathematics, Algorithms and Applications;2023-05-31
4. Double Roman Domination: A Survey;Mathematics;2023-01-09
5. On [k]-Roman domination subdivision number of graphs;AKCE International Journal of Graphs and Combinatorics;2022-09-02