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...

Yuan-Tseh Lee, former president of Academia Sinica and Nobel Prize Winner, opened the second conference of the Council of National Associations with a call to scientists the world-over to come together and confront ever-deepening global problems. Some of the most serious challenges facing mankind -climate change, energy crisis, and disease – stem from processes that transcend national boundarie...

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.

Human appropriation of net primary production (HANPP), the aggregate impact of land use on biomass available each year in ecosystems, is a prominent measure of the human domination of the biosphere. We present a comprehensive assessment of global HANPP based on vegetation modeling, agricultural and forestry statistics, and geographical information systems data on land use, land cover, and soil ...

The issue that this paper addresses is whether we live in a network society and what spatial implications networking has for society. A network is the inner structure of a self-organising system comprised of parts, their relationships/interactions and the patterns that emerge from the interactions. Space is made by all internal structures of a system that are delimited by a system border from a...

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G− v is less than the total domination number of G. We call these graphs total domination critical or just γt-critical. If such a graph G has total domination number k, we call it k-γt-critical. We study an open problem of ...

The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msdγt(G) of a graph G and we show that for any connected graph G of order at least two, msdγt(G) ≤ 3. We show that...

The concept of edge domination is introduced by Mitchell and Hedetniemi [6]. Further results on edge domination are given in Arumugam and Velammal [2]. Functional generalization for vertex subsets has been studied extensively in literature [4, 5]. Cockayne and Mynhardt [3] have introduced that edge subsets may also be embedded into sets of functions and an analogous concept of convexity could a...