Abstract
Let
G
be a finite graph with
p
vertices and
χ
its chromatic polynomial. A combinatorial interpretation is given to the positive integer
(
-
1
)
p
χ
(
-
λ
)
, where
λ
is a positive integer, in terms of acyclic orientations of
G
. In particular,
(
-
1
)
p
χ
(
-
1
)
is the number of acyclic orientations of
G
. An application is given to the enumeration of labeled acyclic digraphs. An algebra of full binomial type, in the sense of Doubilet–Rota–Stanley, is constructed which yields the generating functions which occur in the above context.
