On The Metric Dimension of Some Operation Graphs

Marsidi Marsidi, Ika Hesti Agustin, Dafik Dafik, Ridho Alfarisi, Hendrik Siswono

Abstract

Let  be a simple, finite, and connected graph. An ordered set of vertices of a nontrivial connected graph  is  and the -vector  represent vertex  that respect to , where  and  is the distance between vertex  and  for . The set  called a resolving set for  if different vertex of  have different representations that respect to . The minimum of cardinality of resolving set of G is the metric dimension of , denoted by . In this paper, we give the local metric dimension of some operation graphs such as joint graph , amalgamation of parachute, amalgamation of fan, and .

Keywords

metric dimension, resolving set, operation graphs.

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References

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DOI: http://dx.doi.org/10.18860/ca.v5i3.5331

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