On Roman Domination in Middle and Splitting Graphs

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Eastern Anatolian Journal of Science
Volume: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 : 106 | Download : 20

Publication Date : 2022-12-15

Article Type : Research Paper

Abstract :For a graph G=insert ignore into journalissuearticles values(V,E);, a Roman dominating functioninsert ignore into journalissuearticles values(RDF); is a function f:V→{0,1,2} having the property that every vertex u for which finsert ignore into journalissuearticles values(u);=0 is adjacent to at least one vertex v for which finsert ignore into journalissuearticles values(v);=2. The weight of an RDF insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(winsert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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

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