Enumeration of unlabelled bicolored graphs by degree parities (Q1361672)

This paper presents the ordinary generating function for counting unlabelled bicolored graphs with a given number of odd-degree vertices of each color in the case where the two color classes have equal cardinality, using a more general result [\textit{K. R. Parthasarathy}, Enumeration of graphs with given partition, Can. J. Math. 20, 40-47 (1968; Zbl 0175.20901)]: the ordinary generating function for an unlabelled bicolored graph with a given degree sequence. The present paper completes an investigation begun in [\textit{S. Tazawa}, Enumeration of bicolored graphs with unequal bipartite cardinalities, J. Fac. Sci. Technol., Kinki Univ. 29, 13-21 (1993; Zbl 0795.05076)].