# The Wiener number of powers of the Mycielskian

@article{Balakrishnan2010TheWN, title={The Wiener number of powers of the Mycielskian}, author={Rangaswami Balakrishnan and S. Francis Raj}, journal={Discuss. Math. Graph Theory}, year={2010}, volume={30}, pages={489-498} }

The Wiener number of a graph G is dened as 1 P u;v2V (G) d(u; v), d the distance function on G. The Wiener number has important applications in chemistry. We determine a formula for the Wiener number of an important graph family, namely, the Mycielskians (G) of graphs G. Using this, we show that for k 1, W ( (S k n)) W ( (T k n)) W ( (P k n )), where Sn, Tn and Pn denote a star, a general tree and a path on n vertices respectively. We also obtain Nordhaus-Gaddum type inequality for the Wienerâ€¦Â

## 2 Citations

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### Self-transformation of trees with a bounded degree of vertices to minimize or maximize the Wiener index

- Mathematics, Computer ScienceProceedings of the Institute for System Programming of RAS
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It is shown that any other tree can be obtained from any tree using only atomic transformations, and the tasks of maximizing and minimizing the Wiener index of a tree with a bounded degree of vertices without changing the set of its vertices are considered.

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