Certified Total Domination in Graphs.

Double domination in some graph operators

Let G be a nontrivial graph. A set D ⊆ V(G) is a double dominating set of G if | \mathrm{N_G} [v] ∩ D| ≥ 2 for every vertex v ∈ V(G), where \mathrm{N_G} [v] represents the closed neighborhood of v. The double domination number of G is the minimum cardinality among all double dominating sets of G. In this paper we...

Certified Weakly Connected Domination in Graphs.

Let G be a simple connected graph. We introduce certified weakly connected domination, where each vertex in a weakly connected dominating set S has either zero or at least two neighbors outside S. We establish fundamental relationships and determine the certified weakly connected domination number \gamma^{wc}_{cer}(G)...

RESILIENT DOMINATION IN GRAPHS

Fundamental properties of the resilient domination number are established and corresponding bounds and explicit formulas for the resilient domination number are obtained.

Bounds on Doubly Connected Fair Dominations in Graphs

. A dominating set 𝐃 of graph 𝐆 = (𝐕, 𝐄) is a doubly connected fair dominating set (dcfd-set) if it satisfies the following conditions: (1) the induced subgraphs < 𝐃 > and < 𝐕\𝐃 > are connected and (2) every vertex not in 𝐃 are dominated by the equal number of vertices from 𝐃 . The dcfd(G) is the minimum cardinality of...

IP DOMINATION IN SEMI-TOTAL POINT GRAPHS AND ITS APPLICATION

Independent domination in central graphs

Let $G$ be a graph with vertex set $V(G)$. A set $I\subseteq V(G)$ is an independent dominating set of $G$ if no two vertices in $I$ are adjacent and every vertex in $V(G)\setminus I$ is adjacent to at least one vertex in $I$. The independent domination number of $G$ is the minimum cardinality among all independent dom...