Open Access


Optimized Evaluation of Mobile Base Station by Modern Topological Invariants

Khalid Hamid1, Muhammad Waseem Iqbal2,*, Muhammad Usman Ashraf3, Ahmed Mohammed Alghamdi4, Adel A. Bahaddad5, Khalid Ali Almarhabi6
1 Department of Computer Science, Superior University, Lahore, 54000, Pakistan
2 Department of Software Engineering, Superior University, Lahore, 54000, Pakistan
3 Department of Computer Science, GC Women University, Sialkot, 53310, Pakistan
4 Department of Software Engineering, College of Computer Science and Engineering, University of Jeddah, 21493, Saudi Arabia
5 Department of Information System, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
6 Department of Computer Science, College of Computing in Al-Qunfudah, Umm Al-Qura University, Makkah, 24381, Saudi Arabia
* Corresponding Author: Muhammad Waseem Iqbal. Email:

Computers, Materials & Continua 2023, 74(1), 363-378.

Received 12 May 2022; Accepted 20 June 2022; Issue published 22 September 2022


Due to a tremendous increase in mobile traffic, mobile operators have started to restructure their networks to offload their traffic. New research directions will lead to fundamental changes in the design of future Fifth-generation (5G) cellular networks. For the formal reason, the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory. Any number that can be uniquely calculated by a graph is known as a graph invariant. During the last two decades, innumerable numerical graph invariants have been portrayed and used for correlation analysis. In any case, no efficient assessment has been embraced to choose, how much these invariants are connected with a network graph. This paper will talk about two unique variations of the hexagonal graph with great capability of forecasting in the field of optimized mobile base station topology in setting with physical networks. Since K-banhatti sombor invariants (KBSO) and Contrharmonic-quadratic invariants (CQIs) are newly introduced and have various expectation characteristics for various variations of hexagonal graphs or networks. As the hexagonal networks are used in mobile base stations in layered, forms called honeycomb. The review settled the topology of a hexagon of two distinct sorts with two invariants KBSO and CQIs and their reduced forms. The deduced outcomes can be utilized for the modeling of mobile cellular networks, multiprocessors interconnections, microchips, chemical compound synthesis and memory interconnection networks. The results find sharp upper bounds and lower bounds of the honeycomb network to utilize the Mobile base station network (MBSN) for the high load of traffic and minimal traffic also.


Hexagonal networks; k-banhatti sombor invariants; maple; network graph; artificial intelligence; contraharmonic-quadratic invariants; honeycomb

Cite This Article

K. Hamid, M. W. Iqbal, M. U. Ashraf, A. M. Alghamdi, A. A. Bahaddad et al., "Optimized evaluation of mobile base station by modern topological invariants," Computers, Materials & Continua, vol. 74, no.1, pp. 363–378, 2023.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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