Molecular Descriptors of Nanotube, Oxide, Silicate, and Triangulene Networks

Muhammad Kamran Siddiqui,Wei Gao

doi:10.1155/2017/6540754

Muhammad Kamran Siddiqui, Wei Gao

Open Access

https://doi.org/10.1155/2017/6540754

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Abstract

A topological index is a real number associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity, or biological activity. The concept of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials was established in chemical graph theory based on vertex degrees. It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical networks. In this paper, we study carbon nanotube networks which are motivated by molecular structure of regular hexagonal lattice and also studied interconnection networks which are motivated by molecular structure of a chemical compound SiO4. We determine hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for some important class of carbon nanotube networks, dominating oxide network, dominating silicate network, and regular triangulene oxide network.

Highlights

Multiprocessor interconnection networks are regularly required to associate a huge number of homogeneously repeated processor-memory matches, each of which is known as a preparing hub
Rather than utilizing a mutual memory, all synchronization and communication between processing nodes for program execution is often done via message passing
The work systems have been perceived as adaptable interconnection systems for massively parallel computing; see [1]

Summary

Introduction

Multiprocessor interconnection networks are regularly required to associate a huge number of homogeneously repeated processor-memory matches, each of which is known as a preparing hub. A topological list Top(G) of graph G is a number with the property that, for each diagram H isomorphic to chart G, Top(H) = Top(G). The idea of topological list originated from work done by Wiener [6] while he was chipping away at breaking point of paraffin. He named this list as way number. One of the oldest topological indices is the first Zagreb index introduced by Gutman and Trinajsticbased on degree of vertices of G in 1972 [4]. Ghorbani and Azimi defined two new versions of Zagreb indices of a graph G in 2012 [2]. For further study of topological indices of various graph families, see [8, 11, 12, 14,15,16,17,18,19,20,21,22,23,24,25,26,27]

Carbon Nanotube Networks

Conclusion