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Classifying a family of symmetric graphs

Published online by Cambridge University Press:  17 April 2009

Sanming Zhou
Sanming Zhou
Affiliation:
Department of Mathematics and Statistics, The University of Western Australia, Perth, WA 6907, Australia, e-mail: smzhou@maths.uwa.edu.au Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia, e-mail: smzhou@ms.unimelb.edu.au
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Abstract

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Let Γ be a G-symmetric graph admitting a nontrivial G-invariant partition ℬ of block size υ. For blocks B, C of ℬ adjacent in the quotient graph Γℬ, let k be the number of vertices in B adjacent to at least one vertex in C. In this paper we classify all possibilities for (Γ Γℬ, G) in the case where k = υ − 1 ≥ 2 and ℬ(α) = ℬ(β) for adjacent vertices α β of Γ where for a vertex of Γ, say γ ∈ B, ℬ(γ) denotes the set of blocks C such that γ is the only vertex in B not adjacent to any vertex in C.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 2 , April 2001 , pp. 329 - 335
Copyright
Copyright © Australian Mathematical Society 2001

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