Some Results on Discrepancies between Metric Dimension and Partition Dimension of a Graph*
نویسنده
چکیده
SOME RESULTS ON DISCREPANCIES BETWEEN METRIC DIMENSION AND PARTITION DIMENSION OF A GRAPH* Muhammad Imran Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Sector H-12, Islamabad, Pakistan [email protected] ABSTRACT. In this paper some infinite regular graphs generated by tilings of the plane by infinite hexagonal grid are considered. It is proved that these graphs have discrepancies between their metric dimension and partition dimension. Also, it is proved that for every 2 ≥ n there exist finite induced subgraphs of these graphs having metric dimension equal to n as well as infinite induced subgraphs with metric dimension equal to three. It is natural to ask for a characterization of graphs having discrepancies between their metric dimension and partition dimension. Mathematics Subject Classification: 05C12
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