Date of Final Oral Examination (Defense)
Type of Culminating Activity
Thesis - Boise State University Access Only
Master of Science in Mathematics
Marion Scheepers, Ph.D.
Liljana Babinkostova, Ph.D.
Samuel Coskey, Ph.D.
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.
Nelson, Spencer M., "The Random Graph and Reciprocity Laws" (2017). Boise State University Theses and Dissertations. 1325.