International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 725-729

A generalization of the dichromatic polynomial of a graph

E. J. Farrell

Department of Mathematics, The University of the West Indies, West Indies, St. Augustine, Trinidad and Tobago

Received 4 December 1980

Copyright © 1981 E. J. Farrell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Subgraph polynomial fo a graph pair (G,H), where HG, is defined. By assigning particular weights to the variables, it is shown that this polynomial reduces to the dichromatic polynomial of G. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial.