Metric Dimension for Line Graph of Some Chemical Structures

Abstract

The metric dimension of a graph is a fundamental parameter that measures the minimum number of vertices to identify all other vertices in the graph uniquely. In the context of chemical structures, where graphs represent molecular entities, the metric dimension becomes a crucial metric for understanding molecular behavior and interactions. A subset T = {t1, t2, …, tk} of nodes of a connected network G is referred to as a revolving set, if for any pair of nodes, l, m ∈ V (G) there exists a node t ∈ T, such that its distances from l and m are different. The smallest cardinality of T is referred to as the metric dimension of G, and the nodes in T constitute a metric basis of G. In this work, we calculate the line graph’s metric dimension for some chemical structures such as hexagon-square chains, linear phenylene structures, and linear heptagonal structures.