Advances and Applications in Discrete Mathematics
Volume 17, Issue 1, Pages 11 - 19
(January 2016) http://dx.doi.org/10.17654/AADMJan2016_011_019 |
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INVERTED DISTANCE AND INVERTED WIENER INDEX
Süleyman Ediz and Murat Cancan
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Abstract: The Wiener index is the sum of distances between all pairs of vertices of a (connected) graph. In this paper, we define two novel graph invariants: the inverted distance and the inverted Wiener index. The inverted distance between any two different vertices uand vof a simple connected graph G is defined as: where Ddenotes the diameter of Gand denotes the distance of the vertices uand v. The inverted Wiener index of a simple connected graph G is defined as: where the sum is taken over unordered pairs of vertices of G. We characterized maximum trees with respect to the inverted Wiener index. |
Keywords and phrases: inverted distance, inverted Wiener index, Wiener index, average inverted distance. |
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