Let G = (V, E) be a graph. A function g : V → [0, 1] is called a global dominating function (GDF ) of G, if for every v ∈ V, g(N [v]) = ∑ u∈N [v] g(u) ≥ 1 and g(N(v)) = ∑ u/ ∈N(v) g(u) ≥ 1. A GDF g of a graph G is called minimal (MGDF ) if for all functions f : V → [0, 1] such that f ≤ g and f(v) 6= g(v) for at least one v ∈ V , f is not a GDF . The fractional global domination number γfg(G) is...

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

In a graph G, a vertex is said to dominate itself and its neighbors. The Domination game is a two player game played on a finite graph. Players alternate turns in choosing a vertex that dominates at least one new vertex. The game ends when no move is possible, that is when the set of chosen vertices forms a dominating set of the graph. One player (Dominator) aims to minimize the size of this se...

The 1993 minus 1988 difference in June plus July total precipitation (mm) from gauge observations (left), North American Regional Reanalysis (NARR) (middle) and Global Reanalysis 1 (right).

We consider a combination of state space partitioning and random search methods for solving deterministic global optimization problem. We assume that function computations are costly and nding global optimum is diicult. Therefore, we may decide to stop searching long before we found a solution close to the optimum. Final reward of the algorithm is deened as the best found function value minus t...