On the Upper Bounds of the Numbers of Perfect Matchings in Graphs with Given Parameters
โ Scribed by Hong Lin; Xiao-feng Guo
- Publisher
- Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2007
- Tongue
- English
- Weight
- 151 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0168-9673
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let G be a connected and simple graph, and let i(G) denote the number of stable sets in G. In this letter, we have presented a sharp upper bound for the i(G)-value among the set of graphs with k cut edges for all possible values of k, and characterized the corresponding extremal graphs as well.
Let G be a bipartite graph with 2n vertices, A its adjacency matrix and K the number of perfect matchings. For plane bipartite graphs each interior face of which is surrounded by a circuit of length 4s + 2, s E { 1,2,. . .}, an elegant formula, i.e. det A = (-1 )nK2, had been rigorously proved by Cv