Abstract
A three-valued function f defined on the vertices of a graph G = ( V, E), f : V → {−1, 0, 1}, is a minus dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every v ϵ V, f( N[ v]⩾1), where N[ v] consists of v and every vertex adjacent to v. The weight of a minus dominating function is f( V) = ∑ f( v), over all vertices v ϵ V. The minus domination number of a graph G, denoted γ −( G), equals the minimum weight of a minus dominating function of G. The upper minus domination number of a graph G, denoted Γ −( G), equals the maximum weight of a minimal minus dominating function of G. In this paper we present a variety of algorithmic results. We show that the decision problem corresponding to the problem of computing γ − (respectively, Γ −) is NP-complete even when restricted to bipartite graphs or chordal graphs. We also present a linear time algorithm for finding a minimum minus dominating function in an arbitrary tree.
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.
