Advances and Applications in Discrete Mathematics
Volume 20, Issue 2, Pages 305 - 320
(March 2019) http://dx.doi.org/10.17654/ |
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VERTEX WEIGHTED WIENER POLYNOMIALS OF THE SUBDIVISION GRAPH AND THE LINE GRAPH OF SUBDIVISION GRAPH OF THE WHEEL GRAPH
Zaheer Ahmad, Muhammad K. Jamil, Mohammad R. Farahani, Sudev Naduvath and Hafiz Muhammad Afzal Siddiqui
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Abstract: The Wiener index of a graph G is the sum of all distances between distinct vertices of the graph G. Singly and doubly vertex weighted Wiener polynomials are generalizations of both vertex weighted Wiener numbers and the ordinary Wiener polynomial. In this paper, we compute the singly and doubly vertex polynomials and their corresponding Wiener numbers of the subdivision graph and the line graph of subdivision graph of the wheel graph. |
Keywords and phrases: subdivision graphs, line graphs, wheel Wiener number, Wiener polynomial, singly and doubly vertex weighted Wiener polynomials.
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