On the roman domination number of generalized Sierpiński graphs

Abstract

A map f : V → {0, 1, 2} is a Roman dominating function on a graph G = (V, E) if for every vertex v ∈ V with f (v) = 0, there exists a vertex u, adjacent to v, such that f (u) = 2. The weight of a Roman dominating function is given by f (V ) = u∈V f (u). The minimum weight of a Roman dominating function on G is called the Roman domination number of G. In this article we study the Roman domination number of Generalized Sierpiński graphs S(G, t). More precisely, we obtain a general upper bound on the Roman domination number of S(G, t) and we discuss the tightness of this bound. In particular, we focus on the cases in which the base graph G is a path, a cycle, a complete graph or a graph having exactly one universal vertex.

On roman domination number of functigraph and its complement

“…-function if it is an RDF for G and f ðVðGÞÞ ¼ γ R ðGÞ: For more details, reader can see (Chambers et al, 2009;Favaron et al, 2009;Hajian & Rad, 2017;Kazemi, 2012;Rad & Volkmann, 2011;Ramezani et al, 2017).…”

The Roman domination number of some special classes of graphs - convex polytopes

“…The Roman domination number was studied for a number of classes of graphs: interval graphs, cographs, asteroidal triple-free graphs and graphs with a d-octopus in [17], corona graphs in [31], grid graphs in [8], generalized Sierpiński graphs in [22], generalized Petersen graphs GP (n, 2) in [28] and GP (n, 3) and GP (n, 4) in [32], cardinal product of paths and cycles in [16,15], strongly chordal graphs in [19] and others.…”

On the General Randić index of polymeric networks modelled by generalized Sierpiński graphs

“…Later, the total chromatic number of generalized Sierpiński graphs was studied in [7] and the strong metric dimension has recently been studied in [5]. The authors of [33] obtained closed formulae for the chromatic, vertex cover, clique and domination numbers of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. More recently, a general upper bound on the Roman domination number of S(G, t) was obtained in [28]. In particular, it was studied the case in which the base graph G is a path, a cycle, a complete graph or a graph having exactly one universal vertex.…”