Abstract
The determination of Hosoya polynomial is the latest scheme, and it provides an excellent and superior role in finding the Weiner and hyper-Wiener index. The application of Weiner index ranges from the introduction of the concept of information theoretic analogues of topological indices to the use as major tool in crystal and polymer studies. In this paper, we will compute the Hosoya polynomial for multiwheel graph and uniform subdivision of multiwheel graph. Furthermore, we will derive two well-known topological indices for the abovementioned graphs, first Weiner index, and second hyper-Wiener index.
Highlights
IntroductionTo read more about the chemical application of Weiner index, see [3,4,5,6], and for its mathematical properties, see [7, 8]
W(G) du,v. (1) u,v∈VTo read more about the chemical application of Weiner index, see [3,4,5,6], and for its mathematical properties, see [7, 8].Milan Randic coined the term hyper-Wiener index WW(G) of G [9] as WW(G) du,v u,v∈V + d2u,v. (2)To read more the properties of hyper-Weiner index, see [9,10,11,12]
Hosoya polynomial was first introduced by Hosoya [13] and it received the attention of a lot of researchers. e same notion was independently put forward by Sagan et al [14] as Weiner polynomial G. e Hosoya polynomial H(G, x) of G is defined as
Summary
To read more about the chemical application of Weiner index, see [3,4,5,6], and for its mathematical properties, see [7, 8]. To read more the properties of hyper-Weiner index, see [9,10,11,12]. En, the above definition of Hosoya polynomial can be expressed as d(G). A significant importance of H(G, x) is that some distance-based topological indices (TIs) such as W(G) and WW(G) of G can be computed from the Hosoya polynomial as. E readers can see the following papers [21,22,23,24,25] for the results on distance-based TIs
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