Metric Dimension for Line Graph of Some Chemical Structures

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Hindustan Institute of Technology and Science‎, ‎Chennai 603 103‎, ‎India

2 Department of Mathematics‎, ‎Saveetha School of Engineering‎, ‎SIMATS‎, ‎Chennai‎, ‎602 105‎, ‎India

3 Department of Mathematics‎, ‎Faculty of Arts and Science‎, ‎Bursa Uludag University‎, ‎Gorukle 16059‎, ‎Turkey

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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References

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Iranian Journal of Mathematical Chemistry
Volume 15, Issue 4
December 2024
Pages 269-282

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