Graphs on which dihedral, quaternion, and abelian groups act vertex and/or edge transitively and applications to tensor products

"The graphs on which dihedral, quaternion, and abelian groups act vertex and/or edge transitivity are completely characterized. The vertex transitive graphs belong to one of three families--the well known circulant graphs, the metacirculant graphs constructured by Alspach and Parsons, and a family constructed using a generalization of Alspach's and Parsons' construction. If one of the selected groups acts both vertex and edge transitively on a graph, then it is shown that the graph is the disjoint union of some number of copies of a given cycle. The graphs on which one of the selected groups acts edge transitively but not vertex transitively fall into two broad--disjoint copies of a complete bipartite graph and disjoint copies of a ""pseudo-cycle,"" a graph which is related to the tensor product of a complete bipartite graph and an even cycle."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Sanders, Robin Sue

Contributors dc:contributor

• Weichsel, Paul M.

• Mathematics

Statement dc:rights

• Copyright 1990 Sanders, Robin Sue

Language dc:language

eng

Identifier

AAI9114399
(UMI)AAI9114399

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/19384