Counting unlabeled k-trees

TL;DR

This paper introduces a novel combinatorial approach to count unlabeled k-trees by leveraging proper colorings and symmetry group actions, providing a new method for enumeration in graph theory.

Contribution

It presents a new counting technique for unlabeled k-trees using colorings and group actions, advancing combinatorial enumeration methods.

Findings

Derived a formula for counting unlabeled k-trees

Connected coloring orbits to symmetry group actions

Enhanced understanding of graph enumeration techniques

Abstract

We count unlabeled k-trees by properly coloring them in k+1 colors and then counting orbits of these colorings under the action of the symmetric group on the colors.