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

In a connected graph G with a vertex v, the eccentricity epsilon(v) 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. 'e eccentric connectivity index of G is defined by xi(G) = Sigma(v is an element of V)(G)d(v)epsilon(v), where d(v) is the degree of the vertex v and epsilon(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. 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. 'e 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.