Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
