Dr Vadim Zverovich

The bondage number of graphs on topological surfaces and Teschner's conjecture (2013)
Presentation / Conference Contribution

Randomized algorithms and upper bounds for multiple domination in graphs and networks (2013)
Presentation / Conference Contribution

We consider four different types of multiple domination and provide new improved upper bounds for the k- and k-tuple domination numbers. They generalize two classical bounds for the domination number and are better than a number of known upper bounds... Read More about Randomized algorithms and upper bounds for multiple domination in graphs and networks.

The bondage number of graphs on topological surfaces and Teschner's conjecture (2013)
Journal Article

The bondage number of a graph is the smallest number of its edges whose removal results in a graph having a larger domination number. We provide constant upper bounds for the bondage number of graphs on topological surfaces, and improve upper bounds... Read More about The bondage number of graphs on topological surfaces and Teschner's conjecture.

Upper bounds for the bondage number of graphs on topological surfaces (2013)
Journal Article

The bondage number b(G) of a graph G is the smallest number of edges of G whose removal results in a graph having the domination number larger than that of G. We show that, for a graph G having the maximum vertex degree Δ(G) and embeddable on an orie... Read More about Upper bounds for the bondage number of graphs on topological surfaces.

On Roman, Global and Restrained Domination in Graphs (2011)
Journal Article

In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible. Moreover, we give upper bounds for the restrained domination and total restrained do... Read More about On Roman, Global and Restrained Domination in Graphs.

Upper bounds for the bondage number of graphs on topological surfaces (2011)
Presentation / Conference Contribution

Discrepancy and signed domination in graphs and hypergraphs (2010)
Journal Article

For a graph G, a signed domination function of G is a two-colouring of the vertices of G with colours +1 and -1 such that the closed neighbourhood of every vertex contains more +1's than -1's. This concept is closely related to combinatorial discrepa... Read More about Discrepancy and signed domination in graphs and hypergraphs.

Discrepancy theory and signed domination in graphs and hypergraphs (2009)
Presentation / Conference Contribution

Upper bounds for α-domination parameters (2009)
Journal Article

We provide a new upper bound for the α-domination number in terms of a parameter α, 0 < α ≤ 1, and graph vertex degrees. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic constructi... Read More about Upper bounds for α-domination parameters.

Discrepancy and signed domination in graphs and hypergraphs (2009)
Presentation / Conference Contribution

The k-tuple domination number revisited (2008)
Journal Article

The following fundamental result for the domination number γ (G) of a graph G was proved by Alon and Spencer, Arnautov, Lovász and Payan: γ (G) ≤ frac(ln (δ + 1) + 1, δ + 1) n, where n is the order and δ is the minimum degree of vertices of G. A simi... Read More about The k-tuple domination number revisited.

Upper bounds for the alpha-domination number (2008)
Presentation / Conference Contribution

A generalised upper bound for the k-tuple domination number (2008)
Journal Article

In this paper, we provide an upper bound for the k-tuple domination number that generalises known upper bounds for the double and triple domination numbers. We prove that for any graph G,γ× k (G) ≤ frac(ln (δ - k + 2) + ln (∑m = 1k - 1 (k - m) over(d... Read More about A generalised upper bound for the k-tuple domination number.

The k-tuple domination number revisited (2007)
Presentation / Conference Contribution

A proof of Rautenbach-Volkmann’s conjecture on k-tuple domination (2006)
Presentation / Conference Contribution

The Computer System GRAPHOGRAPH (2006)
Journal Article

The computer system GRAPHOGRAPH (2006)
Presentation / Conference Contribution

A generalised upper bound for the k-tuple domination number (2005)
Presentation / Conference Contribution

Dr Vadim Zverovich's Outputs (92)