Enumeration of unlabelled bicolored graphs by degree parities
β Scribed by Shinsei Tazawa; Teruhiro Shirakura
- Book ID
- 104340255
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 515 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
β¦ Synopsis
This paper gives an ordinary generating function for unlabelled bicolored graphs with a given number of odd vertices, where the cardinalities of the bipartite sets are equal. Moreover, the generating functions for the cardinality of each bipartite set from 1 to 8 are listed.
π SIMILAR VOLUMES
Counting formulae are obtained for the numbers of Itbelled (p,q)-multigraphs with any even number n of points of odd degree and p-n points of even degree. Similar results are obtained for multigraphs of strength s, and in this case for the sum over the ntimber q of lines. These sums are much less si
We show that the number of labeled (n, q)-multigraphs with some specified p vertices of odd degree is asymptotically independent of p and is in fact asymptotically 2'-" times the number of (n, q)-multigraphs. We determine the asymptotic number of (n, q)-multigraphs.