Abstract
A digraph D is homogeneously embedded in a digraph H if for each vertex x of D and each vertex y of H, there exists an embedding of D in H as an induced subdigraph with x at y. A digraph F of minimum order in which D can be homogeneously embedded is called a frame of D and the order of F is called the framing number of D. Several general results involving frames and framing numbers of digraphs are established. The framing number is determined for a number of classes of digraphs, including a class of digraphs whose underlying graph is a complete bipartite graph, a class of digraphs whose underlying graph is C n + K 1, and the lexicographic product of a transitive tournament and a vertex transitive digraph. A relationship between the diameters of the underlying graphs of a digraph and its frame is determined. We show that every tournament has a frame which is also a tournament.
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.