✦ LIBER ✦
Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors
✍ Scribed by Y. O. Hamidoune; A. Lladó; S. C. López
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 148 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex and its neighbors will be called vosperian. Let be a vertex-transitive graph of degree d with order at least d +4. We give necessary and sufficient conditions for the vosperianity of . Moreover, assuming that distinct vertices have distinct neighbors, we show that is vosperian if and only if it is superconnected. Let G be a group and let