- Eastern Anatolian Journal of Science
- Vol: 8 Issue: 2
- On Roman Domination in Middle and Splitting Graphs
On Roman Domination in Middle and Splitting Graphs
Authors : Betül Atay Atakul
Pages : 31-36
View : 14 | Download : 6
Publication Date : 2022-12-15
Article Type : Research
Abstract :For a graph G=(V,E), a Roman dominating function(RDF) is a function f:V→{0,1,2} having the property 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 an RDF ((w(f)) is the sum of assignments for all vertices. The minimum weight of an Roman dominating function on graph G is the Roman domination number, denoted by γ_R (G). In this paper, we study on this variant of the domination number for middle, splitting and Mycielski graphs of some special graphs.Keywords : Graph vulnerability, domination, Roman domination.