Malaysian Journal of Mathematical Sciences, June 2025, Vol. 19, No. 2
On Examining Metric Dimension Through Edge Contraction in Certain Families of Graphs
Saleem, H., Husin, M. N., Ali, S., and Hameed, M. S.
Corresponding Email: nazri.husin@umt.edu.my
Received date: 10 May 2024
Accepted date: 26 December 2024
Abstract:
In graph theory, the Metric Dimension (MD) is an elementary metric
that affords evidence nearly the essential selves of graphs. We reconnoiter the MD in the venue of edge-contracted regular graphs in this paper, with exceptional devotion to the Antiprism, Petersen,
and Harary graphs. Our effort creates a vital bond between antiprism and its edge-contracted counterpart: we give a scheme to regulate the MD of the edge-contracted graph, given the MD of the novel graph. We likewise inspect how edge contraction affects regular graphs' MDs, providing insight into how this operation deviations both the MD and the underlying graph topology. By providing supportive means for the exploration and alteration of regular graphs in a variety of real-world circumstances, our investigation elucidates these belongings and improves the field of graph theory.
Keywords: edge contraction; metric dimension; antiprism graph; Petersen graph; Harary graph
