Indirect counting tress in linear graphs
โ Scribed by Guido Guardabassi
- Book ID
- 103084962
- Publisher
- Elsevier Science
- Year
- 1971
- Tongue
- English
- Weight
- 465 KB
- Volume
- 291
- Category
- Article
- ISSN
- 0016-0032
No coin nor oath required. For personal study only.
โฆ Synopsis
The problem of counting spanning trees in linear graphs is dealt with. A quite general indirect approach, based on the analysis of the complementary graph, is followed and a new counting formula, which applies to any kind of linear non-oriented graph, is given. The paper ends with some comments and concluding remarks.
๐ SIMILAR VOLUMES
A general formula is derivedfor the matching polynomial of an arbitrary graph G. This yields a methodfor counting matchings in graphs. From the general formula, explicit formulae are deducedfor the number of k-matchings in several well-known families of graphs.
We show that any k-regular bipartite graph with 2n vertices has at least \ (k&1) k&1 k k&2 + n perfect matchings (1-factors). Equivalently, this is a lower bound on the permanent of any nonnegative integer n\_n matrix with each row and column sum equal to k. For any k, the base (k&1) k&1 รk k&2 is l