Publication Date

8-2017

Date of Final Oral Examination (Defense)

5-9-2017

Type of Culminating Activity

Thesis - Boise State University Access Only

Degree Title

Master of Science in Mathematics

Department

Mathematics

Major Advisor

Marion Scheepers, Ph.D.

Advisor

Liljana Babinkostova, Ph.D.

Advisor

Samuel Coskey, Ph.D.

Abstract

The theory of random graphs, that is graphs generated by some prescribed random process, gained popularity in the late 1950s and the level of interest has only increased since then. Random graphs on a countably infinite set of vertices is the subject of this thesis. We show that almost all graphs on countably many vertices are isomorphic to each other, implying that there is only one random graph, namely the random graph, on countably many vertices (up to isomorphism). We will survey some historical results concerning the random graph, present a number of its graph theoretic properties, as well as explicit examples based on familiar concepts.

DOI

https://doi.org/10.18122/B28D9N

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