The Merrifield–Simmons index in (n,n+ 1)-graphs
✍ Scribed by Hanyuan Deng; Shubo Chen; Jie Zhang
- Book ID
- 106419366
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 248 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0259-9791
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The Hosoya index and the Merrifield-Simmons index of a graph are defined as the total number of the matchings (including the empty edge set) and the total number of the independent vertex sets (including the empty vertex set) of the graph, respectively. Let W n,k be the set of connected graphs with
## Abstract A graph is said to be __K__~1,__n__~‐free, if it contains no __K__~1,__n__~ as an induced subgraph. We prove that for __n__ ⩾ 3 and __r__ ⩾ __n__ −1, if __G__ is a __K__~1,__n__~‐free graph with minimum degree at least (__n__^2^/4(__n__ −1))__r__ + (3__n__ −6)/2 + (__n__ −1)/4__r__, the