Abstract
In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V (G )i s ak-tuple dominating set of G if each vertex of G is dominated by at least k vertices of S .A k-tuple dominating set S of a graph G is perfect if each vertex of G is dominated by exactly k vertices in S. The k-tuple domination number γ×k(G) is the minimum cardinality among all k-tuple dominating sets of G. In this note we determine the 3-tuple domination number γ×3 for the complete grid graphs Pn × Pm for 2 ≤ n ≤ 4 and m ≥ 1. We also study the existence and construction of perfect 3-tuple dominating sets in this graphs.
Sign-in/Register to access full text options 
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.
