Metric Dimension for Line Graph of Some Chemical Structures

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Nithya Raj R.; Sundara Rajan R.; Rajasingh Indra; Cangul Ismail Naci

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Journal Paper

Paper Information

Journal: Iranian Journal of Mathematical Chemistry Year:2024 | Volume:15 | Issue:4 Page(s): 269-282

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Information Journal Paper

Title

Metric Dimension for Line Graph of Some Chemical Structures

Author(s)

Nithya Raj R. | Sundara Rajan R. | Rajasingh Indra | Cangul Ismail Naci | Issue Writer Certificate

Keywords

Metric basis

Metric dimension

Cyclic hexagonal‎- ‎square chain‎

Linear phenylene structure

Linear heptagonal structure

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 $T = \{ t_1,t_2,\ldots‎, ‎t_k \}$ of nodes of a connected network $G$ is referred to as a revolving set‎, ‎if for any pair of nodes‎, ‎$ l,m \in V(G)$ there exists a node $t \in T$‎, ‎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.

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