Almost Covers Of 2-Arc Transitive Graphs |
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Authors: | Email author" target="_blank">Sanming?ZhouEmail author |
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Institution: | (1) Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia |
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Abstract: | Let be a G-symmetric graph whose vertex set admits a nontrivial G-invariant partition with block size v. Let
be the quotient graph of relative to and B,C] the bipartite subgraph of induced by adjacent blocks B,C of . In this paper we study such graphs for which
is connected, (G, 2)-arc transitive and is almost covered by in the sense that 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
K
v+1 is covered by results of Gardiner and Praeger. We consider here the general case where
K
v+1, and prove that, for some even integer n 4,
is a near n-gonal graph with respect to a certain G-orbit on n-cycles of
. 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
of a graph with these properties. (A near n-gonal graph is a connected graph of girth at least 4 together with a set of n-cycles of such that each 2-arc of is contained in a unique member of .) |
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Keywords: | 05C25 05E99 |
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