Metric Dimension of Maple Leaf Graph
DOI:
https://doi.org/10.24036/eksakta/vol27-iss01/622Keywords:
Metric dimension, resolving set, maple leaf graphAbstract
This study determines the metric dimension of the Maple Leaf Graph (Mₚ) for 2 ≤ p ≤ 9 using the concepts of vertex distance and resolving sets. By analyzing the distance representation of each vertex with respect to a resolving set, the minimum resolving set is identified, defining the metric dimension of the graph. Calculations were performed manually to ensure consistency and accuracy.The analysis reveals a tiered linear reduction pattern, where the metric dimension does not increase linearly with p. The main findings are summarized in three theorems: for p = 2 and p = 3, the metric dimension of the Maple Leaf Graph equals p; for p = 4, 5, and 6, it equals p – 1; and for p = 7, 8, and 9, it equals p – 2. These results introduce a new class of graphs and provide theoretical insights into the behavior of metric dimension in multi-cycle constructions, thereby contributing to the development of combinatorial graph theory.
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