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A class of symmetric graphs with 2-arc transitive quotients

✍ Scribed by Bin Jia; Zai Ping Lu; Gai Xia Wang

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
179 KB
Volume
65
Category
Article
ISSN
0364-9024

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✦ Synopsis

Let be an X -symmetric graph admitting an X -invariant partition B on V ( ) such that B is connected and (X , 2)-arc transitive. A characterization of ( , X , B) was given in [S. Zhou Eur J Comb 23 (2002), 741-760] for the case where |B|>| (C)∩B| = 2 for an arc (B, C) of B . We consider in this article the case where |B|>| (C)∩B| = 3, and prove that can be constructed from a 2-arc transitive graph of valency 4 or 7 unless its connected components are isomorphic to 3K 2 , C 6 or K 3,3 . As a byproduct, we prove that each connected tetravalent (X , 2)-transitive graph is either the complete graph K 5 or a near n-gonal graph for some n β‰₯ 4. α­§ 2010 Wiley

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