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The Dichromate and Orientations of a Graph

Published online by Cambridge University Press:  20 November 2018

Gerald Berman
Gerald Berman*
Affiliation:
University of Waterloo, Waterloo, Ontario
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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 .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 947 - 956
Copyright
Copyright © Canadian Mathematical Society 1977

References

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