Constructing a Class of Symmetric Graphs

In this: publication
By this: publisher
In this Subject: <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: Zhou S.

Author: Zhou S.

Source: European Journal of Combinatorics, Volume 23, Number 6, August 2002 , pp. 741-760(20)

Buy & download fulltext article:

Price: $52.63 plus tax (Refund Policy)

Abstract:

We find a natural construction of a large class of symmetric graphs from point- and block-transitive 1-designs. The graphs in this class can be characterized as G -symmetric graphs whose vertex sets admit a G-invariant partition B of block size at least 3 such that, for any two blocks B, C of B, either there is no edge between B and C, or there exists only one vertex in B not adjacent to any vertex inC. The special case where the quotient graph _Bof relative to Bis a complete graph occurs if and only if the 1-design needed in the construction is a G -doubly transitive and G-block-transitive 2-design, and in this case we give an explicit classification of when G is a doubly transitive projective group or an affine group containing the affine general group. Examples of such graphs include cross ratio graphs studied recently by Gardiner, Praeger and Zhou and some other graphs with vertices the (point, line)-flags of the projective or affine geometry. Copyright 2002 Elsevier Science Ltd. All rights reserved.