Almost Covers Of 2-Arc Transitive Graphs
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- 作者：Sanming Zhou
- 关键词：Mathematics Subject Classification (2000) ; 05C25 ; 05E99
- 刊名：Combinatorica
- 出版年：2004
- 出版时间：September 2004
- 年：2004
- 卷：24
- 期：4
- 页码：731-745
- 全文大小：264 KB
文摘
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 .)