MathDB

Let

V = \left\{ 1, \dots, 8 \right\}

. How many permutations

\sigma : V \to V

are automorphisms of some tree?
(A \emph{graph} consists of some set of vertices and some edges between pairs of distinct vertices. It is \emph{connected} if every two vertices in it are connected by some path of one or more edges. A \emph{tree}

G

V

is a connected graph with vertex set

V

and exactly

|V|-1

edges, and an \emph{automorphism} of

G

is a permutation

\sigma : V \to V

such that vertices

i,j \in V

are connected by an edge if and only if

\sigma(i)

and

\sigma(j)

are.)

Problem Statement