Neumann polynomial

Graph families defined by their automorphisms
distance-transitive	$\to$	distance-regular	$\leftarrow$	strongly regular
$\downarrow$
symmetric (arc-transitive)	$\leftarrow$	t-transitive, t ≥ 2
$\downarrow$(if connected)
vertex- and edge-transitive	$\to$	edge-transitive and regular	$\to$	edge-transitive
$\downarrow$		$\downarrow$		$\downarrow$
vertex-transitive	$\to$	regular	$\to$	(if bipartite) biregular
$\uparrow$
Cayley graph		skew-symmetric		asymmetric