18 citations · 46 across the 68 of their papers we have counts for
18 papers · 1 filter
Relating -Rainbow Domination to Roman domination
José D. Alvarado, Simone Dantas, Dieter Rautenbach
For a graph , let and denote the Roman domination number of and the -rainbow domination number of , respectively. It is known that $γ_{r2}(G)\leq…
Dominating Sets inducing Large Components in Maximal Outerplanar Graphs
José D. Alvarado, Simone Dantas, Dieter Rautenbach
For a maximal outerplanar graph of order at least , Matheson and Tarjan showed that has domination number at most . Similarly, for a maximal outerplanar graph $…
Burning a Graph is Hard
Anthony Bonato, Jeannette Janssen, Elham Roshanbin
Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagio…
Exponential Domination in Subcubic Graphs
Stéphane Bessy, Pascal Ochem, Dieter Rautenbach
As a natural variant of domination in graphs, Dankelmann et al. [Domination with exponential decay, Discrete Math. 309 (2009) 5877-5883] introduce exponential domination, where ver…
Bounds on the Burning Number
Stéphane Bessy, Anthony Bonato, Jeannette Janssen +1
Motivated by a graph theoretic process intended to measure the speed of the spread of contagion in a graph, Bonato, Janssen, and Roshanbin [Burning a Graph as a Model of Social Con…
Bounds on the Exponential Domination Number
Stephane Bessy, Pascal Ochem, Dieter Rautenbach
As a natural variant of domination in graphs, Dankelmann et al. [Domination with exponential decay, Discrete Math. 309 (2009) 5877-5883] introduce exponential domination, where ver…