TY - JOUR

T1 - Computing Eccentricity-Based Topological Indices of 2-Power Interconnection Networks

AU - Imran, Muhammad

AU - Iqbal, Muhammad Azhar

AU - Liu, Yun

AU - Baig, Abdul Qudair

AU - Khalid, Waqas

AU - Zaighum, Muhammad Asad

N1 - Publisher Copyright:
© 2020 Muhammad Imran et al.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.1155/2020/3794592

DO - 10.1155/2020/3794592

M3 - Article

AN - SCOPUS:85087552895

SN - 2090-9063

VL - 2020

JO - Journal of Chemistry

JF - Journal of Chemistry

M1 - 3794592

ER -