Calculating topological indices of certain OTIS interconnection networks

Adnan Aslam,Muhammad Ahsan Binyamin,Safyan Ahmad,Wei Gao

doi:10.1515/chem-2019-0029

Abstract

AbstractRecently, increasing attention has been paid to The Optical Transpose Interconnection System (OTIS) network because of its prospective applications in architectures for parallel as well as distributed systems [27, 28]. Different interconnection networks in the context of topological indices are researched recently in [25, 26]. This article includes the computions of the general Randi´c, first and second Zagreb, general sum connectivity, first and second multiple zagreb, hyper zagreb, ABC and GA indices for OTIS (swapped and biswapped) networks by taking path and k-regular graph on n vertices as a base graphs. In addition, some delicated formulas are also obtained for the ABC4 and GA5 indices for the OTIS biswapped networks by considering basis graph as a path and k-regular graph of order n.

Highlights

Introduction and PreliminariesAs a new emerging science, Cheminformatics is related to chemistry, mathematics and computer sciences, whose major components include Quantitative structure-activity (QSAR) and structure-property relationships (QSPR) and the components can contribute to the research on physicochemical properties of chemical compounds.As a numeric quantity, a topological index is closely related to a graph which is invariant under graph automorphism and can characterize the topology of a graph.Numerous applications of graph theory can be found in structural chemistry
Recently, increasing attention has been paid to The Optical Transpose Interconnection System (OTIS) network because of its prospective applications in architectures for parallel as well as distributed systems [27, 28]
This article includes the computions of the general Randic, first and second Zagreb, general sum connectivity, first and second multiple zagreb, hyper zagreb, Atom-bond connectivity (ABC) and geometric arithmetic (GA) indices for OTIS networks by taking path and k-regular graph on n vertices as a base graphs

Summary

Introduction and Preliminaries

As a new emerging science, Cheminformatics is related to chemistry, mathematics and computer sciences, whose major components include Quantitative structure-activity (QSAR) and structure-property relationships (QSPR) and the components can contribute to the research on physicochemical properties of chemical compounds. Where λ is a balanced parameter adjusted to the specific applications in chemical engineering (generally speaking, λ always takes a value in interval [−20, 20]); the first term ∑︀uv∈E(G)(du + dv) is the first Zagreb index described in (4). By means of derivation, the octanol-water partition coefficient of octanes can be formulated as follows: swapped network with a complete graph of order 6 (K6) as the basis graph. The paper is structured below: In Section 2, we compute the Randić, first and second Zagreb , hyper Zagreb, first and second multiple Zagreb, general sum connectivity, ABC, ABC4, GA and GA5 indices for OTIS swapped networks by taking path and k-regular graphs on n vertices as a base graph.

Results for OTIS Swapped networks OPn

Topological indices of Biswapped networks

Conclusion