Author:
Ahangar Hossein Abdollahzadeh,Amjadi Jafar,Chellali Mustapha,Kosari Saeed,Samodivkin Vladimir,Sheikholeslami Seyed Mahmoud
Abstract
Let G = (V, E) be a simple graph with vertex setxs V and edge set E. A mixed Roman dominating function of G is a function f : V ∪ E → {0, 1, 2} satisfying the condition that every element x ∈ V ∪ E for which f(x) = 0 is adjacent or incident to at least one element y ∈ V ∪ E for which f(y) = 2. The weight of a mixed Roman dominating function f is ω(f) = ∑x∈V∪E f(x). The mixed Roman domination number γR(G) of G is the minimum weight of a mixed Roman dominating function of G. We first show that the problem of computing γR*(G) is NP-complete for bipartite graphs and then we present upper and lower bounds on the mixed Roman domination number, some of them are for the class of trees.
Funder
Babol Noshirvani University of Technology
Subject
Management Science and Operations Research,Computer Science Applications,Theoretical Computer Science
Cited by
1 articles.
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1. Varieties of Roman domination II;AKCE International Journal of Graphs and Combinatorics;2020-07-13