|
Título:
|
Vertex-transitive graphs that remain connected after failure of a vertex an its neighbors
|
|
Autor/a:
|
Hamidoune, Yahya ould; Lladó Sánchez, Ana M.; López Masip, Susana Clara
|
|
Otros autores:
|
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
|
Abstract:
|
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 $\Gamma$ be a vertex-transitive graph of degree d with order at least d+4. We give
necessary and sufficient conditions for the vosperianity of $\Gamma$. Moreover, assuming that distinct vertices have distinct neighbors, we show that $\Gamma$ is vosperian if and only if it is superconnected. Let G be a group and let S⊂G\{1} with S=$S^{-1}$.We show that the Cayley graph, Cay(G,S), defined on G by S is vosperian if and only if G\(S∪{1}) is not a progression and for every non-trivial subgroup H and every a∈G,
|(H∪Ha)(S∪{1})|≥min(|G|−1, |H∪Ha|+|S|+1).
If moreover S is aperiodic, then Cay(G,S) is vosperian if and only if it is superconnected. |
|
Materia(s):
|
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
-Cayley graphs
-Atom
-Calculus of variations
-Grafs, Teoria de
-Àtoms
-Càlcul de variacions |
|
Derechos:
|
|
|
Tipo de documento:
|
Artículo - Versión publicada
Artículo |
|
Editor:
|
Wiley InterScience
|
|
Compartir:
|
|
