Upper bounds for alpha-domination parameters
arXiv:0805.0612 · doi:10.1007/s00373-009-0864-6
Abstract
In this paper, we provide a new upper bound for the alpha-domination number. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic construction is used to generalise another well-known upper bound for the classical domination in graphs. We also prove similar upper bounds for the alpha-rate domination number, which combines the concepts of alpha-domination and k-tuple domination.
7 pages; Presented at the 4th East Coast Combinatorial Conference, Antigonish (Nova Scotia, Canada), May 1-2, 2008