Metric Dimension of the Pinwheel Subdivision Graph K_1+mK_3

Abstract

Metric dimension is an important concept in graph theory that is widely used in various fields, including navigation, network localization, and network design. The concept of metric dimension is the concept of determining the least marker vertex so that each vertex in the graph is distinguished from each other. The purpose of this research is to determine the metric dimension of the pinwheel subdivision graph ????1+????????3. The type of research used is pure research. By using graph structure and vertex distance analysis, this paper shows the value of the metric dimension of the subdivision graph ????(????,????), specifically on the pinwheel graph ????=????1+????????3 for 2≤????≤4. The results show that the metric dimension of the pinwheel subdivision graph ????1+????????3 is one less than the metric dimension of the pinwheel graph before subdivision, ????????????(????(????,????))=????????????(????)−1.