Open Access

ARTICLE

Comparative Study of Valency-Based Topological Descriptor for Hexagon Star Network

Ali N. A. Koam¹, Ali Ahmad^2,*, M. F. Nadeem³

1 Department of Mathematics, College of Science, Jazan University, New Campus, Jazan, 2097, Saudi Arabia
2 College of Computer Science & Information Technology Jazan University, Jazan, Saudi Arabia
3 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000, Pakistan

* Corresponding Author: Ali Ahmad. Email:

Computer Systems Science and Engineering 2021, 36(2), 293-306. https://doi.org/10.32604/csse.2021.014896

Received 25 October 2020; Accepted 13 November 2020; Issue published 05 January 2021

Abstract

A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena. The structure of an interconnection network can be represented by a graph. In the network, vertices represent the processor nodes and edges represent the links between the processor nodes. Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks. A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism. There are various uses of graph theory in the field of basic science. The main notable utilization of a topological descriptor in science was by Wiener in the investigation of paraffin breaking points. In this paper we study the topological descriptor of a newly design hexagon star network. More preciously, we have computed variation of the Randic' R', fourth Zagreb M₄, fifth Zagreb M₅, geometric-arithmetic G A, atom-bond connectivity ABC, harmonic H, symmetric division degree SDD, first redefined Zagreb, second redefined Zagreb, third redefined Zagreb, augmented Zagreb AZI, Albertson A, Irregularity measures, Reformulated Zagreb, and forgotten topological descriptors for hexagon star network. In the analysis of the quantitative structure property relationships (QSPRs) and the quantitative structure activity relationships (QSARs), graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds. We also gave the numerical and graphical representations comparisons of our different results.

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