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- Tomasz Bartnicki, Bostjan Bresar, Jaroslaw Grytczuk, Matjaz Kovse, Zofia Miechowicz, Iztok Peterin
- Electr. J. Comb.
- 2007

The game chromatic number χg is considered for the Cartesian product G 2 H of two graphs G and H. We determine exact values of χg(G2H) when G and H belong to certain classes of graphs, and show that, in general, the game chromatic number χg(G2H) is not bounded from above by a function of game chromatic numbers of graphs G and H. An analogous result is… (More)

- Florent Foucaud, Eleonora Guerrini, Matjaz Kovse, Reza Naserasr, Aline Parreau, Petru Valicov
- Eur. J. Comb.
- 2011

An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of minimum possible size turned out to be a challenging problem. It was proved by N. Bertrand, I. Charon, O. Hudry and A.… (More)

- Kannan Balakrishnan, Bostjan Bresar, +4 authors Ajitha R. Subhamathi
- Discrete Applied Mathematics
- 2009

A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x ∈ V (G) the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary… (More)

- Sandi Klavzar, Matjaz Kovse
- Eur. J. Comb.
- 2007

The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. It is proved that for arbitrary graphs G and J and a positive integer r ≥ 2, there exists a connected graph H such that G is the… (More)

- Laurent Beaudou, Sylvain Gravier, Sandi Klavzar, Matjaz Kovse, Michel Mollard
- Discrete Mathematics & Theoretical Computer…
- 2010

For a graph G and integers a and b, an (a, b)-code of G is a set C of vertices such that any vertex from C has exactly a neighbors in C and any vertex not in C has exactly b neighbors in C. In this paper we classify integers a and b for which there exists (a, b)-codes in Sierpiński graphs.

Geodetic sets in graphs are briefly surveyed. After an overview of earlier results, we concentrate on recent studies of the geodetic number and related invariants in graphs. Geodetic sets in Cartesian products of graphs and in median graphs are considered in more detail. Algorithmic issues and relations with several other concepts, arising from various… (More)

- Sylvain Gravier, Matjaz Kovse, Michel Mollard, Julien Moncel, Aline Parreau
- Des. Codes Cryptography
- 2013

In this paper we study identifying codes, locating-dominating codes, and total-dominating codes in Sierpiński graphs. We compute the minimum size of such codes in Sierpiński graphs.

- Wilfried Imrich, Matjaz Kovse
- Eur. J. Comb.
- 2009

The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. In this note we prove that for every connected graph G there exists a graph H such that G is a convex subgraph of H and V (G) is the… (More)