IJPAM: Volume 108, No. 4 (2016)
HONEYCOMB DERIVED NETWORKS
Department of Mathematics
Chennai, 600 034, INDIA
Abstract. For a vertex of a connected graph and a subset of , the distance between and , denoted by , is . Let = be an ordered -partition of . The representation of with respect to is the -vector = . The -partition is a resolving partition if the -vectors , for all are distinct. The minimum for which there is a resolving -partition of is called the partition dimension of . In this paper, we determine partition dimension of Hive network, Honeycomb rhombic mesh, Honeycomb rectangular mesh.
Received: January 19, 2016
AMS Subject Classification: 05C12
Key Words and Phrases: resolving partition, partition dimension, hive network, honeycomb rhombic mesh, honeycomb rectangular mesh
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DOI: 10.12732/ijpam.v108i4.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 809 - 818