Abstract
Topological indices are the numbers associated with the graphs of chemical compounds/networks that help us to understand their properties. The aim of this paper is to compute topological indices for the hierarchical hypercube networks. We computed Hosoya polynomials, Harary polynomials, Wiener index, modified Wiener index, hyper-Wiener index, Harary index, generalized Harary index, and multiplicative Wiener index for hierarchical hypercube networks. Our results can help to understand topology of hierarchical hypercube networks and are useful to enhance the ability of these networks. Our results can also be used to solve integral equations.
Highlights
Being a hierarchical structure, the hierarchical hypercube (HHC) bears the advantages usually gained by hierarchy [24]
The HHC bears the advantages usually gained by hierarchy [24]
The performance of HHC is in the worst case equivalent to the performance of the connected cycle (CCC) [29,30,31,32,33,34]. e number of vertices and edges in (HHC − 1) is 16a + 16 and 24a + 20, respectively, where a is a natural number. e number of vertices and edges in (HHC − 2) is 16a + 16 and 32a + 28, respectively. (HHC − 1) and (HHC − 2) are shown in Figures 1 and 2, respectively
Summary
We give the definitions and known results that are used in proving main results of this paper. E Wiener index for a simple connected graph G is denoted by W(G) and is defined as the sum of distances between all pairs of vertices in G, i.e., W(G) 1 d(y, z). For a simple connected graph G, the hyper-Wiener index is denoted by WW(G) and is defined as WW(G) 1 d(y, z) + d(y, z)2. For a simple connected graph G, the modified Wiener index is defined as WWλ(G). E Harary polynomial for a simple connected graph G is denoted by h(G) and is defined as h(G) . E generalized Harary index for a simple connected graph G is denoted by ht(G) and is defined as ht(G). E multiplicative Wiener index for a simple connected graph G is denoted by π(G) and is defined as π(G) d(y, z) Definition 8 (multiplicative Wiener index). e multiplicative Wiener index for a simple connected graph G is denoted by π(G) and is defined as π(G) d(y, z)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
