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Results in Mathematics

, 74:173 | Cite as

Quasi-total Roman Domination in Graphs

  • Suitberto Cabrera García
  • Abel Cabrera Martínez
  • Ismael G. YeroEmail author
Article
  • 57 Downloads

Abstract

A quasi-total Roman dominating function on a graph \(G=(V, E)\) is a function \(f : V \rightarrow \{0,1,2\}\) satisfying the following:
  • Every vertex u for which \(f(u) = 0\) is adjacent to at least one vertex v for which \(f(v) =2\), and

  • If x is an isolated vertex in the subgraph induced by the set of vertices labeled with 1 and 2, then \(f(x)=1\).

The weight of a quasi-total Roman dominating function is the value \(\omega (f)=f(V)=\sum _{u\in V} f(u)\). The minimum weight of a quasi-total Roman dominating function on a graph G is called the quasi-total Roman domination number of G. We introduce the quasi-total Roman domination number of graphs in this article, and begin the study of its combinatorial and computational properties.

Keywords

Quasi-total Roman domination number Roman domination number total Roman domination number 

Mathematics Subject Classification

05C69 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Estadística e Investigación Operativa Aplicadas y CalidadUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Departament d’Enginyeria Informàtica i MatemàtiquesUniversitat Rovira i VirgiliTarragonaSpain
  3. 3.Departamento de Matemáticas, Escuela Politécnica Superior de AlgecirasUniversidad de CádizAlgecirasSpain

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