Abstract
For a subset W of vertices of an undirected graph G, let S( W) be the subgraph consisting of W, all edges incident to at least one vertex in W, and all vertices adjacent to at least one vertex in W. If there exists a W such that S( W) is a tree containing all the vertices of G, then S( W) is a spanning star tree of G. These and associated notions are related to connected and/or acyclic dominating sets and also arise in the study of A-trails in Eulerian plane graphs. Among the results in this paper are a characterization of those values of n and m for which there exists a connected graph with n vertices and m edges that has no spanning star tree, and a proof that finding spanning star trees is in general NP-hard.
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.