Roman Domination in Mycielski Graphs: A Study of Some Graphs and a Heuristic Algorithm

Let G= (V, E) be a graph. A function f: V→\0, 1, 2\, if ∀u for which f (u) =0 is adjacent to ∃v for which f (v) =2, is called a Roman dominating function, and called in short terms RDF. The weight of an RDF f is f (V) =∑_ (v∈V) ▒f (v). The Roman domination number of a graph G, denoted by γR (G), is the minimum weight of an RDF on G. This paper presents the results for Roman domination numbers of the Mycielski graphs obtained through Mycielski's construction of the comet, double comet, and comb graphs. An algorithm to determine the Roman domination number of any given graph is also provided.