Construction for trees without domination critical vertices

Abstract

Denote by γ(G) the domination number of graph G. A vertex v of a graph G is called fixed if v belongs to every minimum dominating set of G, and bad if v does not belong to any minimum dominating set of G. A vertex v of G is called critical if γ(G−v)<γ(G). By using these notations of vertices, we give a construction for trees that does not contain critical vertices.

Keywords

• tree
• domination
• critical vertex
• fixed vertex
• bad vertex