Wiener Indices and Polynomials of Five Graph Operators
نویسندگان
چکیده
The sum of distances between all vertices pairs in a connected graph is known as the Wiener Index. It is the earliest of the indices that correlates well with many physicochemical properties of organic compounds and as such has been well-studied over the last quarter of a century. A q-analogue of this index, termed the Wiener Polynomial by Hosoya but also known today as the Hosoya Polynomial, extends this concept by trying to capture the complete distribution of distances in the graph. The mathematicians have studied several operators on a connected graph in which we see a subdivision of the edges. Herein we show how the Wiener Index of a graph changes with these operations, and extend the results to Wiener Polynomials.
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