Total domination supercritical graphs with respect to relative complements
TW Haynes, MA Henning, LC Van Der Merwe - Discrete Mathematics, 2002 - Elsevier
TW Haynes, MA Henning, LC Van Der Merwe
Discrete Mathematics, 2002•ElsevierA set S of vertices of a graph G is a total dominating set if every vertex of V (G) is adjacent to
some vertex in S. The total domination number γ t (G) is the minimum cardinality of a total
dominating set of G. Let G be a connected spanning subgraph of K s, s, and let H be the
complement of G relative to K s, s; that is, K s, s= G⊕ H is a factorization of K s, s. The graph
G is k-supercritical relative to K s, s if γ t (G)= k and γ t (G+e)= k− 2 for all e∈ E (H).
Properties of k-supercritical graphs are presented, and k-supercritical graphs are …
some vertex in S. The total domination number γ t (G) is the minimum cardinality of a total
dominating set of G. Let G be a connected spanning subgraph of K s, s, and let H be the
complement of G relative to K s, s; that is, K s, s= G⊕ H is a factorization of K s, s. The graph
G is k-supercritical relative to K s, s if γ t (G)= k and γ t (G+e)= k− 2 for all e∈ E (H).
Properties of k-supercritical graphs are presented, and k-supercritical graphs are …
Abstract
A set S of vertices of a graph G is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γt(G) is the minimum cardinality of a total dominating set of G. Let G be a connected spanning subgraph of Ks,s, and let H be the complement of G relative to Ks,s; that is, Ks,s=G⊕H is a factorization of Ks,s. The graph G is k-supercritical relative to Ks,s if γt(G)=k and γt(G+e)=k−2 for all e∈E(H). Properties of k-supercritical graphs are presented, and k-supercritical graphs are characterized for small k.
Elsevier
Showing the best result for this search. See all results