Abstract
Assigning numbers to graphs serves as a fundamental tool in graph theory and enables various analytical, computational, and visualization techniques for studying and understanding graph structures and properties. Edge Contraction is a process that separates edges from the graph while also joining the two previously linked vertices. In this paper, we study metric dimension and degree-based topological indices of Möbius Ladder and edge contracted Möbius Ladder like first Zagreb index, second Zagreb index, first Zagreb Hyper index, second Zagreb Hyper index, Augmented Zagreb index, Randic index, general Randic index, and Harmonic index.
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