81 citations · 214 across the 80 of their papers we have counts for
10 papers · 2 filters
Distribution of global defensive -alliances over some graph products
Mostafa Tavakoli, Sandi Klavžar
If is a graph, then is a global defensive -alliance in if (i) each vertex not in has a neighbor in and (ii) each vertex of has at…
Exact distance graphs of product graphs
Boštjan Brešar, Nicolas Gastineau, Sandi Klavžar +1
Given a graph , the exact distance- graph has as its vertex set, and two vertices are adjacent whenever the distance between them in equals .…
Maker-Breaker domination number
Valentin Gledel, Vesna Iršič, Sandi Klavžar
The Maker-Breaker domination game is played on a graph by Dominator and Staller. The players alternatively select a vertex of that was not yet chosen in the course of the g…
Packing chromatic vertex-critical graphs
Sandi Klavžar, Douglas F. Rall
The packing chromatic number of a graph is the smallest integer such that the vertex set of can be partitioned into sets , , where vertices in $…
The variety of domination games
Boštjan Brešar, Csilla Bujtás, Tanja Gologranc +6
Domination game [SIAM J.\ Discrete Math.\ 24 (2010) 979--991] and total domination game [Graphs Combin.\ 31 (2015) 1453--1462] are by now well established games played on graphs by…
Lower bounds for dilation, wirelength, and edge congestion of embedding graphs into hypercubes
R. Sundara Rajan, Thomas Kalinowski, Sandi Klavžar +2
Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. One of the most efficient interconnection networks is…
M-Polynomial Revisited: Bethe Cacti and an Extension of Gutman's Approach
Emeric Deutsch, Sandi Klavžar
The -polynomial of a graph is defined as , where , , is the number of edges of such that $\{d_v(G), d_u(G)\} =…
Domination game and minimal edge cuts
Sandi Klavžar, Douglas F. Rall
In this paper a relationship is established between the domination game and minimal edge cuts. It is proved that the game domination number of a connected graph can be bounded abov…
Strong geodetic cores and Cartesian product graphs
Valentin Gledel, Vesna Iršič, Sandi Klavžar
The strong geodetic problem on a graph is to determine a smallest set of vertices such that by fixing one shortest path between each pair of its vertices, all vertices of a…
Cutting Lemma and Union Lemma for the Domination Game
Paul Dorbec, Michael A. Henning, Sandi Klavžar +1
Two new techniques are introduced into the theory of the domination game. The cutting lemma bounds the game domination number of a partially dominated graph with the game dominatio…