Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516174 | Journal of Combinatorial Theory, Series B | 2005 | 21 Pages |
Abstract
This paper forms part of a study of 2-arc transitivity for finite imprimitive symmetric graphs, namely for graphs Î admitting an automorphism group G that is transitive on ordered pairs of adjacent vertices, and leaves invariant a nontrivial vertex partition B. Such a group G is also transitive on the ordered pairs of adjacent vertices of the quotient graph ÎB corresponding to B. If in addition G is transitive on the 2-arcs of Î (that is, on vertex triples (α,β,γ) such that α,β and β,γ are adjacent and αâ γ), then G is not in general transitive on the 2-arcs of ÎB, although it does have this property in the special case where B is the orbit set of a vertex-intransitive normal subgroup of G. On the other hand, G is sometimes transitive on the 2-arcs of ÎB even if it is not transitive on the 2-arcs of Î. We study conditions under which G is transitive on the 2-arcs of ÎB. Our conditions relate to the structure of the bipartite graph induced on BâªC for adjacent blocks B,C of B, and a graph structure induced on B. We obtain necessary and sufficient conditions for G to be transitive on the 2-arcs of one or both of Î,ÎB for certain families of imprimitive symmetric graphs.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Mohammad A. Iranmanesh, Cheryl E. Praeger, Sanming Zhou,