Journal of Combinatorics
Volume 8 (2017)
Note on “hook-length” as a graph invariant of trees
Pages: 209 – 226
The hook-length of a vertex $v$ in a rooted tree $T$, analogous to that defined in the Ferrers diagrams of integer partitions, is the number of descendants of $v$ (including $v$ itself) in $T$. In this note we consider two different types of “average” hook-length of vertices in a rooted tree, yielding a graph invariant that has interesting correlation to the distance functions in trees. This correlation is observed and used throughout the study of related properties and extremal questions.