Subtrees of graphs

作者：Alex Chin, Gary Gordon, Kellie J. MacPhee, C.H. Vincent · 发表于：Journal of Graph Theory · 年份：2018 · DOI：10.1002/jgt.22359 · 被引用次数：29 · 研究领域：Graph theory and applications、Molecular spectroscopy and chirality、Computational Drug Discovery Methods

Abstract We 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.