June 10, 2023 # Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences

## Research

 Title Strong Roman Domination Number of Complementary Prism Graphs Type Article Keywords Strong Roman domination, double Roman domination, Roman domination, prism, complementary prism, differential of a graph Journal Turkish Journal of Mathematics and Computer Science DOI — Researchers a { color: #4f98b0; } a:hover { color: #ffab00; } a:link:visited { text-decoration: none; } Doost Ali Mojdeh (First researcher) , Ali Parsian (Second researcher) , Iman Masoumi (Third researcher)

## Abstract

Let G = (V; E) be a simple graph with vertex set V = V(G), edge set E = E(G) and from maximum degree  = (G). Also let f : V ! f0; 1; :::; d2 e + 1g be a function that labels the vertices of G. Let Vi = fv 2 V : f (v) = ig for i = 0; 1 and let V2 = V 􀀀 (V0 S V1) = fw 2 V : f (w)  2g. A function f is called a strong Roman dominating function (StRDF) for G, if every v 2 V0 has a neighbor w, such that w 2 V2 and f (w)  1 + d 1 2 jN(w) T V0je. The minimum weight, !( f ) = f (V) = v2V f (v), over all the strong Roman dominating functions of G, is called the strong Roman domination number of G and we denote it by S tR(G). An StRDF of minimum weight is called a S tR(G)-function. Let G be the complement of G. The complementary prism GG of G is the graph formed from the disjoint union G and G by adding the edges of a perfect matching between the corresponding vertices of G and G. In this paper, we investigate some properties of Roman, double Roman and strong Roman domination number of GG.