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A group distance magic labeling of a graph G(V, E) with |V | = n is an injection from V to an abelian group Γ of order n such that the sum of labels of all neighbors of every vertex x ∈ V is equal to the same element µ ∈ Γ. We completely characterize all Cartesian products C k 2C m that admit a group distance magic labeling by Z km .

- Sylwia Cichacz-Przenioslo, Dalibor Froncek, Petr Kovár
- IWOCA
- 2009

- Myra B. Cohen, Charles J. Colbourn, Dalibor Froncek
- COCOON
- 2001

- Michael Kubesa, Dalibor Froncek
- Discussiones Mathematicae Graph Theory
- 2006

- Dan Archdeacon, Joanna A. Ellis-Monaghan, +5 authors Raphael Yuster
- Journal of Graph Theory
- 2004

8 We give two results on domination in graphs, including a proof of a conjecture of Favaron, Henning, Mynhart and Puech [2]. Corollary 2 was found by four separate subsets of the authors. We decided to give this joint presentation of our results. We first offer a result about bipartite graphs. Lemma 1 Let G be a bipartite graph with partite sets (X, Y)… (More)

- Dalibor Froncek, Petr Kovár, Tereza Kovarova, Michael Kubesa
- Discrete Mathematics
- 2010

- Dalibor Froncek, Alexander Rosa, Jozef Sirán
- Eur. J. Comb.
- 1996

All values of n for which there exist a selfcomplementary circulant graph of order n are determined. Let G be a finite , simple , undirected graph. The graph G is selfcompletementary if G is isomorphic to its complement G ; in symbols , G Ӎ G . It is well known that a selfcomplementary graph of order n exists if f n ϵ 0 or 1 (mod 4). Moreover , a regular… (More)

- Sergei L. Bezrukov, Dalibor Froncek, Steven J. Rosenberg, Petr Kovár
- Discrete Mathematics
- 2008

It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bi-partite graph K n,n with a perfect matching removed can be covered by k bicliques, then n ≤ k k 2. We give a slightly simplified proof and we show that the result is tight. Moreover we use the result to prove analogous bounds for coverings of some other classes of graphs by… (More)

- Dalibor Froncek
- Discussiones Mathematicae Graph Theory
- 2004

We examine decompositions of complete graphs with an even number of vertices, K 2n , into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings… (More)

- Dalibor Froncek, Janja Jerebic, Sandi Klavzar, Petr Kovár
- Combinatorics, Probability & Computing
- 2007

The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner's Theorem, the strong isometric dimension of the Hamming graphs K 2 K n is determined.