In this paper some further properties of the coefficients of a chromatic generating function introduced by Linial are proved. A combinatorial interpretation of these numbers is given by specializing some results of Stanley on posets to surjective n-colorings of a graph G of order n compatible with linear orders on V(G) which extend acyclic orientations of G. If G is composed from n isolated vertices these coefficients are classical Eulerian numbers A(n, k). © 1987.
Tomescu, I. (1987). Graphical Eulerian numbers and chromatic generating functions. Discrete Mathematics, 66(3), 315–318. https://doi.org/10.1016/0012-365X(87)90109-9