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Title:
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Vertex-transitive graphs that remain connected after failure of a vertex an its neighbors
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Author:
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Hamidoune, Yahya ould; Lladó Sánchez, Ana M.; López Masip, Susana Clara
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions |
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Abstract:
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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. |
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Subject(s):
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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 |
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Rights:
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Document type:
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info:eu-repo/semantics/publishedVersion
Article |
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Published by:
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Wiley InterScience
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