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 this paper, we prove a common fixed point theorem for six mappings (two set valued and four single valued mappings) without assuming compatibility and continuity of any mapping on non complete metric spaces. to prove the theorem, we use a non compatible condition, that is, weak commutativity of type (kb). we show that completeness of the whole space is not necessary for the existence and uni...

We analyze the domination game, where two players, Dominator and Staller, construct together a dominating set M in a given graph, by alternately selecting vertices into M . Each move must increase the size of the dominated set. The players have opposing goals: Dominator wishes M to be as small as possible, and Staller has the opposite goal. Kinnersley, West and Zamani conjectured in [4] that wh...

The last years there is an increasing interest for query processing techniques that take into consideration the dominance relationship between objects to select the most promising ones, based on user preferences. Skyline and top-k dominating queries are examples of such techniques. A skyline query computes the objects that are not dominated, whereas a top-k dominating query returns the k object...

Let p be a positive integer andG= (V ,E) a graph. A subset S of V is a p-dominating set if every vertex of V − S is dominated at least p times, and S is a p-dependent set of G if the subgraph induced by the vertices of S has maximum degree at most p − 1. The minimum cardinality of a p-dominating set a ofG is the p-domination number p(G) and the maximum cardinality of a p-dependent set ofG is th...

In a graph G = (V (G), E(G)), a vertex dominates itself and its neighbors. A subset S of V (G) is a double dominating set if every vertex of V (G) is dominated at least twice by the vertices of S. The double domination number of G is the minimum cardinality among all double dominating sets of G. We consider the effects of edge removal on the double domination number of a graph. We give a necess...

A {em Roman dominating function} on a graph $G$ is a function$f:V(G)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}A {em restrained Roman dominating}function} $f$ is a {color{blue} Roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} The wei...

Let ω denote the set of natural numbers. For functions f, g : ω → ω, we say that f is dominated by g if f(n) < g(n) for all but finitely many n ∈ ω. We consider the standard “fair coin” probability measure on the space 2 of infinite sequences of 0’s and 1’s. A Turing oracle B is said to be almost everywhere dominating if, for measure one many X ∈ 2, each function which is Turing computable from...