Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

8-2008

Committee Chair or Co-Chairs

Robert A. Beeler

Committee Members

Anant P. Godbole, Robert B. Gardner, Teresa W. Haynes

Abstract

Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As a cycle with at least four vertices is a canonical example of a triangle-free subgraph, we concentrate our efforts on these. In this thesis, we will state necessary and sufficient conditions for the existence of edge induced and vertex induced cycles within circulants.

Document Type

Thesis - Open Access

Copyright

Copyright by the authors.

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