Bounds on Weak Roman and 2-Rainbow Domination Numbers
We mainly study two related dominating functions, namely, the weak Roman and 2-rainbow dominating functions. We show that for all graphs, the weak Roman domination number is bounded above by the 2-rainbow domination number. We present bounds on the weak Roman domination number and the secure domination number in terms of the total domination number for specific families of graphs, and we show that the 2-rainbow domination number is bounded below by the total domination number for trees and for a subfamily of cactus graphs.
Chellali, Mustapha; Haynes, Teresa W.; and Hedetniemi, Stephen T.. 2014. Bounds on Weak Roman and 2-Rainbow Domination Numbers. Discrete Applied Mathematics. Vol.178 27-32. https://doi.org/10.1016/j.dam.2014.06.016 ISSN: 0166-218X