Vertex Domination Critical Graphs
Abbreviated Journal Title
Computer Science; Hardware & Architecture; Operations Research; Management Science
A dominating set in a graph G is a set of vertices D such that every vertex of G is either in D or is adjacent some vertex of D. The domination number Γ(G) of G is the minimum cardinality of any dominating set. A graph is vertex domination‐critical if the removal of any vertex decreases its domination number. This paper gives examples and properties of vertex domination‐critical graphs, presents a method of constructing them, and poses some open questions. In the process several results for arbitrary graphs are presented.
Brigham, Robert C.; Chinn, Phyllis Z.; and Dutton, Ronald D., "Vertex Domination Critical Graphs" (1988). Faculty Bibliography 1980s. 963.