Metric Dimension of Maple Leaf Graph

Welyyanti, Des
Mulyani Putri, Susi
Pratama Sandy, Ikhlas

Eksakta : Berkala Ilmiah Bidang MIPA
Vol. 27 No. 01 (2026): Eksakta : Berkala Ilmiah Bidang MIPA (E-ISSN : 2549-7464) In Progress

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.