Total roman domination in graphs

Hossein Abdollahzadeh Ahangar, Michael A. Henning, Vladimir Samodivkin, Ismael G. Yero

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)

Abstract

A Roman dominating function on a graph G is a function f: V (G) (0, 1, 2) satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function f is the sum, ΤuΙV(G)f(u), of the weights of the vertices. The Roman domination number is the minimum weight of a Roman dominating function in G. A total Roman domination function is a Roman dominating function with the additional property that the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex. The total Roman domination number is the minimum weight of a total Roman domination function on G. We establish lower and upper bounds on the total Roman domination number. We relate the total Roman domination to domination parameters, including the domination number, the total domination number and Roman domination number.

Original languageEnglish
Pages (from-to)501-517
Number of pages17
JournalApplicable Analysis and Discrete Mathematics
Volume10
Issue number2
DOIs
Publication statusPublished - 2016

Keywords

  • Domina-tion
  • Roman domination
  • Total Roman domination
  • Total domination

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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