COMPLEMENTARY TREE PAIRED DOMINATION VERTEX CRITICAL GRAPHS

Majority domination vertex critical graphs

This paper deals the graphs for which the removal of any vertex changes the majority domination number of the graph. In the following section, how the removal of a single vertex fromG can change the majority domination number is surveyed for trees. Characterisation of V + M (G) and V − M (G) are determined.

Diameter of paired domination edge-critical graphs

A paired dominating set of a graph G without isolated vertices is a dominating set of G whose induced subgraph has a perfect matching. The paired domination number γpr(G) of G is the minimum cardinality amongst all paired dominating sets of G. The graph G is paired domination edge-critical (γprEC) if for every e ∈ E(G), γpr(G+ e) < γpr(G). We investigate the diameter of γprEC graphs. To this ef...

Vertex Domination Critical in Circulant Graphs

Complementary Tree Domination in Splitting Graphs of Graphs

Let G = (V, E) be a simple graph. A dominating set D is called a complementary tree dominating set if the induced subgraph is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of G and is denoted by ctd(G). For a graph G, let V(G) = {v : v  V(G)} be a copy of V(G). The splitting graph Sp(G) of G is the graph with ...

Paired-Domination Game Played in Graphs

In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...