The Metric Dimension and Local Metric Dimension of Relative Prime Graph

Inna Kuswandari, Fatmawati Fatmawati, Mohammad Imam Utoyo

Abstract


This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo  integer rings, namely . As a vertex set is  and  if  and  are relatively prime. By finding the pattern elements of resolving set and local resolving set, it can be shown the value of the metric dimension and the local metric dimension of graphs  are  and  respectively, where  is the number of vertices groups that formed multiple 2,3, … ,  and  is the cardinality of set . This research can be developed by determining the value of the fractional metric dimension, local fractional metric dimension and studying the advanced properties of graphs related to their forming rings.

Key Words : metric dimension; modulo ; relative prime graph; resolving set; rings.

Keywords


Graph Theory

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DOI: https://doi.org/10.18860/ca.v6i3.10103

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