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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 $…
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
Boštjan Brešar, María 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 Sierpiński 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 close…
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…
Graphs with span 1 and shortest optimal walks
Tanja Dravec, Mirjana Mikalački, Andrej Taranenko
A span of a given graph is the maximum distance that two players can keep at all times while visiting all vertices (edges) of and moving according to certain rules, that pr…