Computing Eccentricity-Based Topological Indices of 2-Power Interconnection Networks

Muhammad Imran,Muhammad Asad Zaighum,Abdul Qudair Baig,Waqas Khalid,Yun Liu,Muhammad Azhar Iqbal

doi:10.1155/2020/3794592

Abstract

In a connected graph G with a vertex v, the eccentricity εv of v is the distance between v and a vertex farthest from v in the graph G. Among eccentricity-based topological indices, the eccentric connectivity index, the total eccentricity index, and the Zagreb index are of vital importance. The eccentric connectivity index of G is defined by ξG = ∑v∈VGdvεv, where dv is the degree of the vertex v and εv is the eccentricity of v in G. The topological structure of an interconnected network can be modeled by using graph explanation as a tool. This fact has been universally accepted and used by computer scientists and engineers. More than that, practically, it has been shown that graph theory is a very powerful tool for designing and analyzing the topological structure of interconnection networks. The topological properties of the interconnection network have been computed by Hayat and Imran (2014), Haynes et al. (2002), and Imran et al. (2015). In this paper, we compute the close results for eccentricity-based topological indices such as the eccentric connectivity index, the total eccentricity index, and the first, second, and third Zagreb eccentricity index of a hypertree, sibling tree, and X-tree for k-level by using the edge partition method.

Highlights

Muhammad Imran,1 Muhammad Azhar Iqbal,2 Yun Liu,3 Abdul Qudair Baig,4 Waqas Khalid,5 and Muhammad Asad Zaighum2
Among eccentricity-based topological indices, the eccentric connectivity index, the total eccentricity index, and the Zagreb index are of vital importance. e eccentric connectivity index of G is defined by ξ(G) = 􏽐v∈V(G)d(v)ε(v), where d(v) is the degree of the vertex v and ε(v) is the eccentricity of v in G. e topological structure of an interconnected network can be modeled by using graph explanation as a tool. is fact has been universally accepted and used by computer scientists and engineers
It has been shown that graph theory is a very powerful tool for designing and analyzing the topological structure of interconnection networks. e topological properties of the interconnection network have been computed by Hayat and Imran (2014), Haynes et al (2002), and Imran et al (2015)

Summary

Introduction

Muhammad Imran ,1 Muhammad Azhar Iqbal,2 Yun Liu,3 Abdul Qudair Baig,4 Waqas Khalid,5 and Muhammad Asad Zaighum2. E eccentric connectivity index of G is defined by ξ(G) = 􏽐v∈V(G)d(v)ε(v), where d(v) is the degree of the vertex v and ε(v) is the eccentricity of v in G. e topological structure of an interconnected network can be modeled by using graph explanation as a tool. We compute the close results for eccentricity-based topological indices such as the eccentric connectivity index, the total eccentricity index, and the first, second, and third Zagreb eccentricity index of a hypertree, sibling tree, and X-tree for k-level by using the edge partition method.

Results

Conclusion