Roman and inverse roman domination in network of triangles

Abstract

In graph G (V, E), a function f : V ? {0, 1 2} is said to be a Roman Dominating Function (RDF). If ?u ? V, f(u) = 0 is adjacent to at least one vertex v ? V such that f(v) = 2. The weight of f is given by w(f) = P v?V f(v). The Roman Domination Number (RDN) denoted by ?R(G) is the minimum weight among all RDF in G. If V ?D contains a RDF f 1 : V ? {0, 1, 2}, where D is the set of vertices v, f(v) > 0, then f 1 is called Inverse Roman Dominating Function (IRDF) on a graph G with respect to the RDF f. The Inverse Roman Domination Number (IRDN) denoted by ? 1 R(G) is the minimum weight among all IRDF in G. In this paper we find RDN and IRDN of few triangulations graphs.