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Dissertation/Thesis Abstract

A Survey of the Degree/Diameter Problem for Undirected Graphs
by Steller, Paul, M.Sc., University of Delaware, 2020, 75; 27993407
Abstract (Summary)

Given a fixed diameter and maximum degree, the degree/diameter problem involves finding the maximum possible order of a graph. The Moore bound represents the upper threshold that such an order may achieve, and only few graphs reach this threshold. In this thesis, we explore these graphs, including the elusive, hypothetical Moore graph of degree 57. This thesis will also examine graphs that fail to achieve equality in the Moore bound by only a few vertices. These graphs also turn out to be scarce. Finally, we look at a related problem, the Moore bipartite bound, and examine graphs that come very close to achieving this upper bound.

Indexing (document details)
Advisor: Cioaba, Sebastian
Commitee: Lazebnik, Felix, Ghandehari, Mahya
School: University of Delaware
Department: Mathematical Sciences
School Location: United States -- Delaware
Source: MAI 82/3(E), Masters Abstracts International
Subjects: Mathematics, Theoretical Mathematics
Keywords: Algebraic graph theory, Degree/diameter problem, Graph theory, Moore graphs, Spectral graph theory
Publication Number: 27993407
ISBN: 9798678106780
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