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.
Let
To read more about the chemical application of Weiner index, see [
Milan Randic coined the term hyper-Wiener index
To read more the properties of hyper-Weiner index, see [
Let
The Hosoya polynomial has been investigated on polycyclic aromatic hydrocarbons [
The readers can see the following papers [
For
Multiwheel graph
Next, the theorem gives the expression for the Hosoya polynomial of
It is easy to observe that the diameter of
The cardinality of order pairs in
The cardinality of the above sets is
The subdivision graph
Uniform subdivision of multiwheel graph
It is easy to observe that order and size of are
It is easy to observe that the diameter of
The cardinality of order pairs in
The cardinality of the above sets is
The cardinality of order pairs in
The cardinality of the above sets is
The cardinality of order pairs in
The cardinality of the above sets is
The cardinality of order pairs in
The cardinality of the above sets is
The cardinality of order pairs in
The cardinality of the above sets is
Now, using the values of
We examined the Hosoya polynomial and two vastly studied TIs
No data were used for this study.
Mathematics subject classification: 05C09, 05C92, 92E10.
The authors hereby declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China, No. 62002079.