# Fowler, Patrick W.

## Fowler's Conjecture on eigenvalues of (3,6)-polyhedra ★★

Author(s): Fowler

\begin{conjecture} Let $G$ be the graph of a $(3,6)$-polyhedron with $2k + 4$ vertices. Then the eigenvalues of $G$ can be partitioned into three classes: $K = \{3, -1, -1, -1\}$, $P = {x_1, ..., x_k\}$ (where $x_i$ is nonnegative for $i = 1, \dots , k$), and $N = - P$. \end{conjecture}

Keywords: (3,6)-polyhedron; eigenvalues