Speaker
Description
Metric dimension is an important concept in graph theory that measures the
ability of a set of vertices to distinguish other vertices through distance. This
research focuses on analyzing the metric dimension of the pinwheel
subdivision graph K1+mK3, a graph consisting of one central vertex K1
connected to m copies of a triangular graph K3, where each edge of the
pinwheel graph is subdivided. Subdivision is adding new vertices that enrich
the graph structure and increase the complexity in calculating the metric
dimension. The purpose of this study is to determine the smallest cardinality
of the pinwheel subdivision graph K1+mK3 for 2≤m≤4. The type of research
used is pure research involving combinatorial analysis of the distance
between vertices in the graph. The results show that the metric dimension of
the pinwheel subdivision graph K1+mK3 has decreased by one unit
compared to the pinwheel graph that does not undergo subdivision. This
finding can enrich the literature related to metric dimension in pinwheel
subdivision graphs and can be applied in various problems related to robot
navigation and sensor system design. Thus, this research makes an
important contribution to the development of graph theory.
