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doi:10.1016/0095-8956(78)90035-7 
Copyright © 1978 Published by Elsevier Inc.
Decomposition of graph functions
Received 15 December 1975.
Available online 3 September 2004.
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Abstract
The V-functions of Tutte [1] are generalized to U-functions on graphs with a distinguished subset of vertices. The class of U-functions of two variables generalize dichromatic polynomials as well as the W-functions defined by Tutte [2]. The values of U-functions on a graph G are characterized in terms of spanning subgraphs of G and also in terms of collections of simple graphs constructed from G. Decompositions of dichromatic polynomials as well as dichromatic U-functions are obtained in terms of decompositions of G.
