Upper bounds for alpha-domination parameters
Andrei Gagarin, Anush Poghosyan, and Vadim E. Zverovich
TL;DR
This paper introduces new upper bounds for alpha-domination parameters in graphs, extending classical bounds and applying probabilistic methods to generalize existing results for domination and alpha-rate domination.
Contribution
It provides generalized upper bounds for alpha-domination and alpha-rate domination numbers, extending classical bounds using probabilistic constructions.
Findings
New upper bounds for alpha-domination number
Generalized bounds for alpha-rate domination
Probabilistic methods applied to domination parameters
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.
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