Domination versus edge domination

Total domination versus paired domination

A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by γt. The maximal size of an inclusionwise minimal total dominating set, the upper total domination num...

Perfect edge domination and efficient edge domination in graphs

Let G = (V; E) be a /nite and undirected graph without loops and multiple edges. An edge is said to dominate itself and any edge adjacent to it. A subset D of E is called a perfect edge dominating set if every edge of E \ D is dominated by exactly one edge in D and an e cient edge dominating set if every edge of E is dominated by exactly one edge in D. The perfect (e cient) edge domination prob...

Edge Domination in Graphs

Let G be a (p, q)-graph with edge domination number γ′ and edge domatic number d′. In this paper we characterize connected graphs for which γ′ = p/2 and graphs for which γ′ + d′ = q + 1. We also characterize trees and unicyclic graphs for which γ′ = bp/2c and γ′ = q −∆′, where ∆′ denotes the maximum degree of an edge in G.

Efficient Domination and Efficient Edge Domination: A Brief Survey

Cn-edge Domination in Graphs

Let G = (V, E) be a graph. A subset D of V is called common neighbourhood dominating set (CN-dominating set) if for every v ∈ V −D there exists a vertex u ∈ D such that uv ∈ E(G) and |Γ(u, v)| > 1, where |Γ(u, v)| is the number of common neighbourhood between the vertices u and v. The minimum cardinality of such CN-dominating set denoted by γcn(G) and is called common neighbourhood domination n...