Abstract

Given a graph G=(V,E) and integer values fv, v∈V, a node subset D⊂V is a total f-dominating set if every node v∈V is adjacent to at least fv nodes of D. Given a weight system c(v), v∈V, the minimum weight total f-dominating set problem is to find a total f-dominating set of minimum total weight. In this article, we propose a polyhedral study of the associated polytope together with a complete and compact description of the polytope for totally unimodular graphs and cycles. We also propose a linear time dynamic programming algorithm for the case of trees.

Full Text

Published Version (Free)

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 call

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.