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


Jia-Bao Liu, Muhammad Imran*, Shakila Baby, Hafiz Muhammad Afzal Siddiqui and Muhammad Kashif Shafiq  


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

Aim and Objective: 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 indies.

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.


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


School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box 15551, Al Ain, Department of Mathematics, Government College University Faisalabad, Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Department of Mathematics, University of Management and Technology, Sialkot campus

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