[HTML][HTML] Total outer-connected domination numbers of trees
Let G=(V, E) be a graph without an isolated vertex. A set D⊆ V (G) is a total dominating set if
D is dominating, and the induced subgraph G [D] does not contain an isolated vertex. The
total domination number of G is the minimum cardinality of a total dominating set of G. A set
D⊆ V (G) is a total outer-connected dominating set if D is total dominating, and the induced
subgraph G [V (G)− D] is a connected graph. The total outer-connected domination number
of G is the minimum cardinality of a total outer-connected dominating set of G. We …
D is dominating, and the induced subgraph G [D] does not contain an isolated vertex. The
total domination number of G is the minimum cardinality of a total dominating set of G. A set
D⊆ V (G) is a total outer-connected dominating set if D is total dominating, and the induced
subgraph G [V (G)− D] is a connected graph. The total outer-connected domination number
of G is the minimum cardinality of a total outer-connected dominating set of G. We …
Let G=(V,E) be a graph without an isolated vertex. A set D⊆V(G) is a total dominating set if D is dominating, and the induced subgraph G[D] does not contain an isolated vertex. The total domination number of G is the minimum cardinality of a total dominating set of G. A set D⊆V(G) is a total outer-connected dominating set if D is total dominating, and the induced subgraph G[V(G)−D] is a connected graph. The total outer-connected domination number of G is the minimum cardinality of a total outer-connected dominating set of G. We characterize trees with equal total domination and total outer-connected domination numbers. We give a lower bound for the total outer-connected domination number of trees and we characterize the extremal trees.
Elsevier