Some Results on the Strong Roman Domination Number of Graphs
نویسندگان
1 Department of Mathematics, Payame Noor University, I. R. Iran
2 Department of Mathematics, Dehloran Branch, University of Applied Science and Technology Dehloran, I. R. Iran
3 Faculty of Mathematical Sciences, University of Tabriz, Tabriz, I. R. Iran
doi
10.22052/mir.2020.225635.1205چکیده
Let G=(V,E) be a finite and simple graph of order n and maximum degree Δ(G). A strong Roman dominating function on a graph G is a function f:V (G)→{0, 1,… ,[Δ(G)/2 ]+ 1} satisfying the condition that every vertex v for which f(v)=0 is adjacent to at least one vertex u for which f(u) ≤ 1+ [(1/2)| N(u) ∩ V0| ], where V0={v ∊ V | f(v)=0}. The minimum of the values ∑v∊ V f(v), taken over all strong Roman dominating functions f of G, is called the strong Roman domination number of G and is denoted by γStR(G). In this paper we continue the study of strong Roman domination number in graphs. In particular, we present some sharp bounds for γStR(G) and we determine the strong Roman domination number of some graphs.
