IJPAM: Volume 108, No. 4 (2016)

PARTITION DIMENSION OF
HONEYCOMB DERIVED NETWORKS

Chris Monica M.$^{1}$, S. Santhakumar$^{2}$
$^{1,2}$Department of Mathematics
Loyola College
Chennai, 600 034, INDIA


Abstract. For a vertex $v$ of a connected graph $G$ and a subset $S$ of $V(G)$, the distance between $v$ and $S$, denoted by $d(v,S)$, is $min$$\{d(v,x)$ $\vert$ $ x\in S \}$. Let $ \Pi $ = $\{S_{1}, S_{2}$ $...$ $S_{k}\}$ be an ordered $k$-partition of $V(G)$. The representation of $v$ with respect to $ \Pi $ is the $k$-vector $r(v\vert\Pi )$ = $(d(v,S_{1}), d(v,S_{2} )$ $...$ $d(v,S_{k} ))$. The $k$-partition is a resolving partition if the $k$-vectors $r(v\vert\Pi )$, for all $v \in V(G)$ are distinct. The minimum $k$ for which there is a resolving $k$-partition of $V(G)$ is called the partition dimension $pd(G)$ of $G$. 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
Year: 2016
Volume: 108
Issue: 4
Pages: 809 - 818


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