9 papers · 1 filter
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…
On the isolation number of graphs with minimum degree four
Wayne Goddard, Michael A. Henning
An isolating set in a graph is a set of vertices such that removing and its neighborhood leaves no edge. The isolation number of (also known as the vertex-ed…
On -coalition in graphs: bounds and exact values
Boštjan Brešar, Michael A. Henning, Babak Samadi
Given a graph $G=\big{(}V(G),E(G)\big{)}$, a set is called a -dominating set if every vertex in has at least neighbors in . Two disjoi…
On polluted bootstrap percolation in Cartesian grids
Boštjan Brešar, Jaka Hedžet, Michael A. Henning
Given a graph and assuming that some vertices of are infected, the -neighbor bootstrap percolation rule makes an uninfected vertex infected if has at least i…
Paired domination in trees: A linear algorithm and asymptotic normality
Michael A. Henning, Dimbinaina Ralaivaosaona
A set of vertices in a graph is a paired dominating set if every vertex of is adjacent to a vertex in and the subgraph induced by contains a perfect matching (n…
Paired domination in graphs with minimum degree four
Csilla Bujtás, Michael A. Henning
A set of vertices in a graph is a paired dominating set if every vertex of is adjacent to a vertex in and the subgraph induced by admits a perfect matching. The…