Browsing by Author "Maktoof, Mohammed Abdul Jaleel"

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Exploring Metric Dimensions in Chemical Structures : Insights and Applications
(Taru Publications, 2025) Chaudhry, Faryal; Maktoof, Mohammed Abdul Jaleel; Mousa, Sura Hamed; Farooq, Umar; Farahani, Mohammad Reza; Alaeiyan, Mehdi; Cancan, Murat
In this article, we dive into the metric dimension of various lattice networks, focusing on Bakelite, Backbone DNA, and Polythiophene networks. The metric dimension is a crucial graph invariant that helps us understand how uniquely we can identify the vertices in a network. Our detailed analysis and calculations reveal that the metric dimension for Bakelite, Polythiophene, and Backbone DNA networks is consistently two. This means that, within these lattice structures, a simple pair of vertices is enough to pinpoint the location of all other vertices. These insights shed light on the structural properties of these molecular networks and could have practical implications for areas like biological systems and organic electronics. Plus, this study sets the stage for future research in graph theory and the understanding of molecular structures.
On Metric Dimension of Circumcoronene Series of Benzenoid Networks
(Taru Publications, 2025) Chaudhry, Faryal; Abbas, Azhar Ali; Maktoof, Mohammed Abdul Jaleel; Farooq, Umar; Farahani, Mohammad Reza; Alaeiyan, Mehdi; Cancan, Murat
In molecular topology and chemistry, resolving sets and metric bases are essential concepts. They have numerous applications in computer science, artificial intelligence, chemistry, pharmacy, traffic networking, mathematical modeling, and programming. Adivision S of the vertex set chi of a linked graph G is said to resolve G if eachpoint of G can be represented from its neighborhood in S. A metric dimension of a graph is the number of the smallest resolving set, also known as the metric basis of the graph.In the current research we will determine the metric dimension and metric basis of the circumcoronene series CS of benzenoid Hk for k >= 1. We prove that a set with three vertices is required to resolve this graph, and therefore, its metric dimension is 3.