Lower bound on the minus-domination number

Lower bound on the minus-domination number

For a graph G, a function f : V (G) ! f?1; 0; +1g is called a minus-domination function of G if the closed neighborhood of each vertex of G contains strictly more

Lower bound on the paired domination number of a tree

Lower bound on the domination number of a tree

We prove that the domination number γ(T ) of a tree T on n ≥ 3 vertices and with n1 endvertices satisfies inequality γ(T ) ≥ n+2−n1 3 and we characterize the extremal graphs.

Lower bounds on the signed (total) $k$-domination number

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...

Minus domination number in k-partite graphs

A function f de1ned on the vertices of a graph G = (V; E); f :V → {−1; 0; 1} is a minus dominating function if the sum of its values over any closed neighborhood is at least one. The weight of a minus dominating function is f(V ) = ∑ v∈V f(v). The minus domination number of a graph G, denoted by −(G), equals the minimum weight of a minus dominating function of G. In this paper, a sharp lower bo...