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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 χ g (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)

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

- 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 ver-tices 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)

- 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 Sierpi´nski graphs. We compute the minimum size of such codes in Sierpi´nski graphs.

- Kannan Balakrishnan, Bostjan Bresar, Manoj Changat, Sandi Klavzar, Matjaz Kovse, Ajitha R. Subhamathi
- Algorithmica
- 2010

The median (antimedian) set of a profile π = (u 1 ,. .. , u k) of vertices of a graph G is the set of vertices x that minimize (maximize) the remoteness i d(x, u i). Two algorithms for median graphs G of complexity O(n idim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles… (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 Sierpi´nski graphs.

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)

- 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)