#### Filter Results:

- Full text PDF available (5)

#### Publication Year

1980

2012

- This year (0)
- Last 5 years (1)
- Last 10 years (5)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

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

- 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

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

- Andrey A. Dobrynin, Leonid S. Melnikov, Artem V. Pyatkin
- Discrete Mathematics
- 2003

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

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

Let G be a 4-regular planar graph and suppose that G has a cycle decomposition S (i.e., each edge of G is in exactly one cycle of the decomposition) with every pair of adjacent edges on a face always in different cycles of S. Such graphs, called Grötzsch–Sachs graphs, arise as a superposition of simple closed curves in the plane with tangencies disallowed.… (More)

- 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.

- Leonid S. Melnikov, Artem V. Pyatkin
- Discrete Mathematics
- 2002

Given a set of integers S; G(S) = (S; E) is a graph, where the edge uv exists if and only if u+ v∈ S. A graph G = (V; E) is an integral sum graph or ISG if there exists a set S ⊂ Z such that G=G(S). This set is called a labeling of G. The main results of this paper concern regular ISGs. It is proved that all 2-regular graphs with the exception of C4 are… (More)

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