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Combinatorial Chemistry & High Throughput Screening

Author(s): Jia-Bao Liu, Muhammad Imran*, Shakila Baby, Hafiz Muhammad Afzal Siddiqui and Muhammad Kashif Shafiq

DOI: 10.2174/1386207324666210217143114

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Graph Indices for Cartesian Product of F-sum of Connected Graphs

Page: [528 - 535] Pages: 8

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Abstract

Background: A topological index is a real number associated with a graph that provides information about its physical and chemical properties and their correlations. Topological indices are being used successfully in Chemistry, Computer Science, and many other fields.

Methods: In this article, we apply the well-known Cartesian product on F-sums of connected and finite graphs. We formulate sharp limits for some famous degree-dependent indices.

Results: Zagreb indices for the graph operations T(G), Q(G), S(G), R(G), and their F-sums have been computed. By using orders and sizes of component graphs, we derive bounds for Zagreb indices, F-index, and Narumi-Katayana index.

Conclusion: The formulation of expressions for the complicated products on F-sums, in terms of simple parameters like maximum and minimum degrees of basic graphs, reduces the computational complexities.

Keywords: F-sum of graphs, Cartesian product, Narumi-Katayana index, Zagreb index, Augmented Zagreb index, F-index.

Graphical Abstract

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