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- Andrey A. Dobrynin, Leonid S. Melnikov
- Discussiones Mathematicae Graph Theory
- 2006

The Wiener index, W , is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of ∆ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown… (More)

- Andrey A. Dobrynin, Leonid S. Melnikov
- Appl. Math. Lett.
- 2005

The Wiener number, W (G), is the sum of the distances of all pairs of vertices in a graph G. Infinite families of graphs with increasing cyclomatic number and the property W (G) = W (L(G)) are presented, where L(G) denotes the line graph of G. This gives a positive (partial) answer to an open question posed in an earlier paper by Gutman, Jovašević, and… (More)

- V. A. Aksionov, Leonid S. Melnikov
- J. Comb. Theory, Ser. B
- 1980

- Andrey A. Dobrynin, Leonid S. Melnikov
- Electronic Notes in Discrete Mathematics
- 2005

- Leonid S. Melnikov, Vadym G. Vizing
- Journal of Graph Theory
- 1999

- V. A. Aksionov, Oleg V. Borodin, Leonid S. Melnikov, Gert Sabidussi, Michael Stiebitz, Bjarne Toft
- J. Comb. Theory, Ser. B
- 2005

It is proved that by deleting at most 5 edges every planar graph can be reduced to a graph having a non-trivial automorphism. Moreover, the bound of 5 edges cannot be lowered to 4.

- Andrey A. Dobrynin, Leonid S. Melnikov
- Journal of Graph Theory
- 2008

- Andrey A. Dobrynin, Leonid S. Melnikov
- Discrete Mathematics
- 2006

- Andrey A. Dobrynin, Leonid S. Melnikov
- Discrete Mathematics
- 2009

- Andrey A. Dobrynin, Leonid S. Melnikov, Artem V. Pyatkin
- Journal of Graph Theory
- 2004