Geodesic
The Dichromate and Orientations of a Graph
Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 947-956

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Internal and external activities are defined for any orientation of a graph relative to a fixed labelling of its edges. It is shown that the number of such orientations of having internal activity r and external activity s is 2r+sXrs where Xrs is the coefficient of xrys in the dichromate It follows that the number of orientations of in which the resulting digraph is acyclic is given by , where is the chromatic polynomial associated with . 
Berman, Gerald. The Dichromate and Orientations of a Graph. Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 947-956. doi: 10.4153/CJM-1977-095-1
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