Access to this thesis is limited to Boise State University students and employees or persons using Boise State University facilities.
Off-campus Boise State University users: To download Boise State University access-only theses/dissertations, please select the "Off-Campus Download" button and enter your Boise State username and password when prompted.
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
Recommended Citation
Nelson, Spencer M., "The Random Graph and Reciprocity Laws" (2017). Boise State University Theses and Dissertations. 1325.
https://doi.org/10.18122/B28D9N