Abstract
A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number γpr(G) is the minimum cardinality of a paired-dominating set of G. In this paper, we prove the conjecture of Goddard and Henning (2009) stating that if G is a connected cubic graph of order n and G is different from the Petersen graph, then γpr(G)≤4n/7.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.