2-HOP ROMAN DOMINATION OF SOME PRODUCT GRAPHS - Akwu, Abolape Deborah; Akpakwu, Ochidoma; Adefokun, Tayo Charles; Hinding, Nurdin (Matematichki Bilten, 2026)
In this paper, we introduce the study of 2-hop Roman dominating functions of some product graphs. A 2-hop Roman dominating (2HRD) function on a graph \(G=(V,E)\)is a function \(f:V(G)→\{0,1,2\}\) such that for every vertex \(v\) with \(f(v)=0\), there are two vertices \(x,y\) with \(f(x)=f(y)=2\) and \(d(v,x)=d(v,y)=2\). The weight of 2HRD function is the sum of its function values over all the vertices. The 2-hop Roman domination number of \(G\) denoted by \(γ_{2hR}(G)\) is the minimum weight of a 2HRD function in \(G\). We present the upper bond of 2-hop Roman domination number of Cartesian product graph. Also, we determine the 2-hop Roman domination number of tensor product graphs.
Keywords: Hop Roman Domination; Domination number; 2- Domination; Roman Domination