Abstract
A set D of vertices of a connected graph G=( V, E) is called a connected k-dominating set of G if every vertex in V– D is within distance k from some vertex of D, and the induced subgraph G[ D] is connected, where k⩾1 is an integer. The connected k-domination number of G, denoted by γ k c( G), is the minimum cardinality of a connected k-dominating set of G. In this paper, we show that for k⩾2, γ k c (G)⩽(2k+1)d k c ( G ̄ ) if both G and G ̄ are connected, where d k c( G) denotes the connected k-domatic number of G, the maximum number of classes in a partition of V into connected k-dominating sets.
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.