Abstract

AbstractWe study a new graph invariant, the sequence of the number of k‐edge subtrees of a graph. We compute the mean subtree size for several classes of graphs, concentrating on complete graphs, complete bipartite graphs, and theta graphs, in particular. We prove that the ratio of spanning trees to all subtrees in approaches , and give a related formula for . We also connect the number of subtrees of that contain a given subtree to the hyperbinomial transform. For theta graphs, we find formulas for the mean subtree size (approximately ) and the mode (approximately ) of the unimodal sequence . The main tool is a subtree generating function.

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.