# The Cycle Spaces of an Infinite Graph

Unfortunately many of the basic results in finite dimensional vector spaces no longer hold in infinite dimensions. Therefore extending the cycle and bond spaces to infinite graphs is not at all a trivial exercise.

This thesis is mainly concerned with the algebraic properties of the cycle and bond spaces of a locally finite, infinite graph. Our approach is to first topologize and then compactify the graph. This allows us to enrich the set of cycles to include infinite cycles. We introduce two cycle spaces and three bond spaces of a locally finite graph and determine the orthogonality relations between them. We also determine the sum of two of these spaces, and derive a version of the Edge Tripartition Theorem.

Advisor:

School:University of Waterloo

School Location:Canada - Ontario

Source Type:Master's Thesis

Keywords:mathematics

ISBN:

Date of Publication:01/01/2006