8 papers
Domination game and total domination game played on Sierpiński graphs
Tanja Dravec, Daniel P. Johnston, Sandi Klavžar
The game domination numbers and , and the game total domination numbers and are investigated on Sierpiński graphs $…
Thresholds for the biased Maker-Breaker domination games
Boštjan Brešar, Csilla Bujtás, Pakanun Dokyeesun +1
In the -biased Maker-Breaker domination game, two players alternately select unplayed vertices in a graph such that Dominator selects and Staller selects vertice…
A proof of the -conjecture for independent domination in cubic graphs
Boštjan Brešar, Tanja Dravec, Michael A. Henning
A set of vertices in a graph is a dominating set of if every vertex not in is adjacent to a vertex in~. An independent dominating set in is a dominating set…
Monophonic number of Kneser graphs and strongly 2-monophonic graphs
BoÅ¡tjan BreÅ¡ar, MarÃa Gracia Cornet, Tanja Dravec
Given a graph a set is called monophonic if every vertex in lies on some induced path between two vertices in . The monophonic number, , of , wh…
Isolation number: Cartesian and lexicographic products and generalized SierpiÅski graphs
Bostjan Bresar, Tanja Dravec, Daniel P. Johnston +3
The isolation number of a graph is the minimum cardinality of a set such that the subgraph induced by the vertices that are not in the union of the clos…
Graphs with unique Grundy dominating sets
Boštjan Brešar, Tanja Dravec
Given a graph consider a procedure of building a dominating set in by adding vertices to one at a time in such a way that whenever vertex is added to there…