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Cyclic Resolving Number of Grid and Augmented Grid Graphs

M.Chris Monica,D.Little Femilin Jana

Published in:   Vol. 2 Issue 2 Date of Publication:   December 2013
Page(s):   112-114 Publisher:   Integrated Intelligent Research (IIR)
DOI:   10.20894/IJCOA. SAI : 2013SCIA316F0985

For an ordered set W = {w1, w2 � wk}  V (G) of vertices, we refer to the ordered k-tuple r(v  W) = (d(v, w1), d(v, w2) � d(v, wk)) as the (metric) representation of v with respect to W. A set W of a connected graph G is called a resolving set of G if distinct vertices of G have distinct representations with respect to W. A resolving set with minimum cardinality is called a minimum resolving set or a basis. The dimension, dim(G), is the number of vertices in a basis for G. By imposing additional constraints on the resolving set, many resolving parameters are formed. In this paper, we introduce cyclic resolving set and find the cyclic resolving number for a grid graph and augmented grid graph.