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 -