Trees with independent Roman domination number twice the independent domination number-Reference-Cited by-同舟云学术

Trees with independent Roman domination number twice the independent domination number

Published:2015-12 Issue:04 Volume:07 Page:1550048
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Chellali Mustapha¹,Rad Nader Jafari²

Affiliation:

1. LAMDA-RO Laboratory, Department of Mathematics, University of Blida. B. P. 270 Blida, Algeria

2. Department of Mathematics, University of Shahrood, Shahrood, Iran

Abstract

A Roman dominating function (RDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] for which [Formula: see text] is adjacent to at least one vertex [Formula: see text] for which [Formula: see text]. The weight of a RDF [Formula: see text] is the value [Formula: see text]. The Roman domination number, [Formula: see text], of [Formula: see text] is the minimum weight of a RDF on [Formula: see text]. An RDF [Formula: see text] is called an independent Roman dominating function (IRDF) if the set [Formula: see text] is an independent set. The independent Roman domination number, [Formula: see text], is the minimum weight of an IRDF on [Formula: see text]. In this paper, we study trees with independent Roman domination number twice their independent domination number, answering an open question.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830915500482

Reference11 articles.

1. Roman domination in graphs

2. Strong equality between the Roman domination and independent Roman domination numbers in trees

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