We prove that partitionable graphs are 2w -2-connected, that this bound is sharp, and prove some structural properties of cutsets of cardinality 2w -2. The proof of the connectivity result is a simple linear algebraic proof.
On the minimal eccentric connectivity indices of graphs
β Scribed by Jianbin Zhang; Bo Zhou; Zhongzhu Liu
- Book ID
- 113567475
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 348 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Hartnell, B.L. and W. Kocay, On minimal neighbourhood-connected graphs, Discrete Mathematics 92 (1991) 95-105. The closed neighbourhood of a vertex u of a graph G is u\* = {v 1 v is adjacent to u} U {u}. G is neighbourhood-connected if it is connected, and G -u' is connected but not complete, for al
A graph G is (n, \*)-connected if it satisfies the following conditions: (1) |V(G)| n+1; (2) for any subset S V(G) and any subset L E(G) with \* |S| +|L| <n\*, G&S&L is connected. The (n, \*)-connectivity is a common extension of both the vertex-connectivity and the edge-connectivity. An (n, 1)-conn