On the total Roman domination stability in graphs

A total Roman dominating function on a graph G is a function satisfying the conditions: (i) every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2; (ii) the subgraph induced by the vertices assigned non-zero values has no isolated vertices. The minimum of over all...

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Bibliographic Details
Published inAKCE international journal of graphs and combinatorics Vol. 18; no. 3; pp. 166 - 172
Main Authors Asemian, Ghazale, Jafari Rad, Nader, Tehranian, Abolfazl, Rasouli, Hamid
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 02.09.2021
Subjects
complexity
roman domination
total roman domination
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Summary:A total Roman dominating function on a graph G is a function satisfying the conditions: (i) every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2; (ii) the subgraph induced by the vertices assigned non-zero values has no isolated vertices. The minimum of over all such functions is called the total Roman domination number The total Roman domination stability number of a graph G with no isolated vertex, denoted by is the minimum number of vertices whose removal does not produce isolated vertices and changes the total Roman domination number of G. In this paper we present some bounds for the total Roman domination stability number of a graph, and prove that the associated decision problem is NP-hard even when restricted to bipartite graphs or planar graphs.
ISSN:0972-8600
2543-3474
DOI:10.1080/09728600.2021.1992257