Subtrees, \(BC\)-Subtrees of Generalized Bethe Trees and Related Questions

Yu Yang1, Hongbo Liu1, Hua Wang2
1School of information, Dalian Maritime University, Dalian, 116026, China
2 Department of Mathematical Sciences, Georgia Southern University Statesboro, GA, 30460, USA

Abstract

Topological indices of graphs, and trees in particular, have been vigorously studied in the past decade due to their many applications in different fields. Among such indices, the number of subtrees (BC-subtrees), along with their variations, have received much attention. In this paper, we provide some new evaluation results related to these two indices on specific structures, such as generalized Bethe trees, Bethe trees, and dendrimers, which are of practical interest. Using generating functions, we also examine the asymptotic behavior of subtree (resp. BC-subtree) density of dendrimers.