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Published in:   Vol. 2 Issue 2 Date of Publication:   December 2013

Extended Roman Domination Number of Hexagonal Networks

Chiranjilal Kujur,D.Antony Xavier

Page(s):   109-111 ISSN:   2278-2397
DOI:   10.20894/IJCOA.101.002.002.010 Publisher:   Integrated Intelligent Research (IIR)

An extended Roman domination function on a graph G=(V,E) is a function satisfying the conditions that (i) every vertex u for which f(u) is either 0 or 1 is adjacent to at least one vertex v for which f(v) =3. (ii) if u and v are two adjacent vertices and if f(u)=0 then f(v)≠0, similarly if f(u)=1 then f(v)≠1. The weight of an extended Roman domination function is the value ( ) Σ ( ) The minimum weight of an extended Roman domination function on graph G is called the extended Roman domination number of G, denoted by ( ).The Hexagonal networks are popular mesh-derived parallel architectures. In this paper we present an upper bound for the extended Roman domination number of hexagonal networks.