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On 4-Valent Symmetric Graphs

✍ Scribed by A. Gardiner; Cheryl E. Praeger

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 261 KB
Volume: 15
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1994.1041

No coin nor oath required. For personal study only.

✦ Synopsis

Let (G) act transitively on incident vertex, edge pairs of the connected 4-valent graph (\Gamma). If a normal subgroup (N) does not give rise to a natural 4-valent quotient (\Gamma_{N}) with (G / N) acting transitively on incident vertex, edge pairs, then either (a) (N) has just one or two orbits on vertices, or (b) (N) has (r \geqslant 3) orbits on vertices and the natural quotient (\Gamma_{N}) is a circuit (C_{r}) (Theorem 1.1). We give a complete classification of the graphs arising in (a) when the normal subgroup (N) is elementary abelian (Theorems 1.2 and 1.3). Case (b), which depends to some extent on case (a), is more technical and is studied in a subsequent paper.

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