Total outer-connected domination numbers of trees Original Research Article

Let image be a graph without an isolated vertex. A set image is a total dominating set if image is dominating, and the induced subgraph image does not contain an isolated vertex. The total domination number of image is the minimum cardinality of a total dominating set of image. A set image is a total outer-connected dominating set if image is total dominating, and the induced subgraph image is a connected graph. The total outer-connected domination number of image is the minimum cardinality of a total outer-connected dominating set of image. 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.