Almost Covers Of 2-Arc Transitive Graphs

Let Γ be a G-symmetric graph whose vertex set admits a nontrivial G-invariant partition ℬ with block size v. Let Γ be the quotient graph of Γ relative to ℬ and Γ[B,C] the bipartite subgraph of Γ induced by adjacent blocks B,C of ℬ. In this paper we study such graphs for which Γ is connected, (G, 2)-arc transitive and is almost covered by Γ in the sense that Γ[B,C] is a matching of v-1 ≥ 2 edges. Such graphs arose as a natural extremal case in a previous study by the author with Li and Praeger. The case Γ K v+1 is covered by results of Gardiner and Praeger. We consider here the general case where Γ K v+1, and prove that, for some even integer n ≥ 4, Γ is a near n-gonal graph with respect to a certain G-orbit on n-cycles of Γ . Moreover, we prove that every (G, 2)-arc transitive near n-gonal graph with respect to a G-orbit on n-cycles arises as a quotient Γ of a graph with these properties. (A near n-gonal graph is a connected graph Σ of girth at least 4 together with a set ℰ of n-cycles of Σ such that each 2-arc of Σ is contained in a unique member of ℰ.)

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sanming Zhou.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zhou, S. Almost Covers Of 2-Arc Transitive Graphs. Combinatorica 24, 731–745 (2004). https://doi.org/10.1007/s00493-004-0044-5

Download citation

Mathematics Subject Classification (2000):

  • 05C25
  • 05E99