In this paper, we provide a new upper bound for the α-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 α-rate domination number, which combines the concepts of...

“Eternal inflation” is often confused with “chaotic inflation”. Moreover, the term “chaotic inflation” is being used in three different meanings (all of them unrelated to eternal inflation). I make some suggestions in an effort to untangle this terminological mess. I also give a brief review of the origins of

in descartes theological writing, he promotes two jointly puzzling theses: t1) god freely creates the eternal truths (i.e. the creation doctrine) and t2) the eternal truths are necessarily true. according to t1 god freely chooses which propositions to make necessary, contingent and possible. however the creation doctrine makes the acceptance of t2 tenuous for the creation doctrine implies that ...

This article is a follow-up of an that describes the proponents eternal functional subordination (EFS). evangelical movement was introduced by George Knight in 1977. The EFS refers to relationship between God Father and Son as authoritative position held Father, while occupies subordinated position. not mainline Protestant churches. find origin their premise Bible well tradition early church. J...

Let γ(G) and ι(G) be the domination and independent domination numbers of a graph G, respectively. Introduced by Sumner and Moorer [23], a graph G is domination perfect if γ(H) = ι(H) for every induced subgraph H ⊆ G. In 1991, Zverovich and Zverovich [26] proposed a characterization of domination perfect graphs in terms of forbidden induced subgraphs. Fulman [15] noticed that this characterizat...

In this note the split domination number of the Cartesian product of two paths is considered. Our results are related to [2] where the domination number of Pm¤Pn was studied. The split domination number of P2¤Pn is calculated, and we give good estimates for the split domination number of Pm¤Pn expressed in terms of its domination number.

We provide a simple constructive characterization for trees with equal domination and independent domination numbers, and for trees with equal domination and total domination numbers. We also consider a general framework for constructive characterizations for other equality problems.