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- Andrei V. Gagarin, Anush Poghosyan, Vadim E. Zverovich
- Discrete Applied Mathematics
- 2013

We consider four different types of multiple domination and provide new improved upper bounds for the kand k-tuple domination numbers. They generalise two classical bounds for the domination number and are better than a number of known upper bounds for these two multiple domination parameters. Also, we explicitly present and systematize randomized… (More)

- Andrei V. Gagarin, Anush Poghosyan, Vadim E. Zverovich
- Graphs and Combinatorics
- 2009

In this paper, we provide a new upper bound for the α-domination number. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic construction is used to generalise another well-known upper bound for the classical domination in graphs. We also prove similar upper bounds for the α-rate domination… (More)

We are looking into variants of a domination set problem in social networks. While randomised algorithms for solving the minimum weighted domination set problem and the minimum α and α-rate domination problem on simple graphs are already present in the literature, we propose here a randomised algorithm for the minimum weighted αrate domination set problem… (More)

- Anush Poghosyan, Vadim E. Zverovich
- Discrete Mathematics
- 2010

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 discrepancy theory as shown by Füredi and Mubayi [J. Combin. Theory, Ser. B 76 (1999) 223–239]. The signed domination… (More)

- Anush Poghosyan
- 2010

- Vadim E. Zverovich, Anush Poghosyan
- Graphs and Combinatorics
- 2011

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 domination numbers for large classes of graphs, and show that, for almost all graphs, the restrained domination… (More)

In this article, we investigate a domination set problem variant on vertex-weighted graphs. In the last few years, several algorithms have been presented for solving the minimum alpha and alpha-rate domination problem (also known as the positive influence dominating sets problem) on simple graphs. We recently proposed an algorithm for alpha-rate domination… (More)

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