On minimum metric dimension of honeycomb networks

Authors:
Paul Manuel;Rajan Bharati;Indra Rajasingh;Chris Monica M
Affiliations:
Department of Information Science, Kuwait University, Kuwait 13060;Department of Mathematics, Loyola College, Chennai, India 600 034;Department of Mathematics, Loyola College, Chennai, India 600 034;Department of Mathematics, Loyola College, Chennai, India 600 034
Venue:
Journal of Discrete Algorithms
Year:
2008

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Abstract

A minimum metric basis is a minimum set W of vertices of a graph G(V,E) such that for every pair of vertices u and v of G, there exists a vertex w@?W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. The honeycomb and hexagonal networks are popular mesh-derived parallel architectures. Using the duality of these networks we determine minimum metric bases for hexagonal and honeycomb networks.