Subtrees, BC-Subtrees of Generalized Bethe Trees and Related Questions

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 (generalized Bethe trees, Bethe trees, dendrimers), which are some of the structures of practical interests. Using 'generating functions', we also examine the asymptotic behavior of subtree (resp. BC-subtree) density of dendrimers.