## ROMAN AND INVERSE ROMAN DOMINATION IN NETWORK OF TRIANGLES

## ROMAN AND INVERSE ROMAN DOMINATION IN NETWORK OF TRIANGLES

*M. K. Kumar, N. Dhanasekar, G. M. A. Prasath, R. Giri*

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## Abstract

In graph G (V, E), a function f : V ! f0; 1 2g is said to be a Roman Dominating Function (RDF). If 8u 2 V; f(u) = 0 is adjacent to at least one vertex v 2 V such that f(v) = 2. The weight of f is given by w(f) = P v2V f(v). The Roman Domina- tion Number (RDN) denoted by R(G) is the minimum weight among all RDF in G. If V ????D contains a RDF f1 : V ! f0; 1; 2g, where D is the set of vertices v, f(v) > 0, then f1 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 1R (G) is the minimum weight among all IRDF in G. In this paper we nd RDN and IRDN of few triangulations graphs.

## Keywords

Domination Number, Roman Domination Number, Inverse Domination Num- ber.