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Factorisation of Finite Groups and Graphs

Title
Factorisation of Finite Groups and Graphs
Funding
ARC | Discovery Projects
Contract (GA) number
DP0449429
Start Date
2004/01/01
End Date
2006/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP0449429

 

  • Primitive decompositions of Johnson graphs

    A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the group preserving the partition is arc-transitive and acts primitively on the parts.

    On generalised Paley graphs and their automorphism groups

    The generalised Paley graphs are, as their name suggests, a generalisation of the Paley graphs, first defined by Paley in 1933 (see \cite{Paley}). They arise as the relation graphs of symmetric cyclotomic association schemes. However, their automorphism groups may be much larger than the groups of the corresponding schemes. We determine the parameters for which the graphs are connected, or equivalently, the schemes are primitive. Also we prove that generalised Paley graphs are sometimes isomo...
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