College
Buchtel College of Arts and Sciences
Date of Last Revision
2025-04-29 12:39:37
Major
Applied Mathematics
Honors Course
498
Number of Credits
3
Degree Name
Bachelor of Science
Date of Expected Graduation
Spring 2025
Abstract
A Moore graph is a simple regular graph, with n vertices, degree d, and diameter k, that satisfies the Moore bound: n = 1 + d (d − 1)k − 1 d − 2 . There are graphs for which the bound is met and in which existence and uniqueness are known. For k = 2 it is known that the Moore bound is achieved for d = 2, 3, 7, with the case of d = 57 conjectured to exist. For k = 3 the bound is achieved for only d = 3 [5]. Due to the construction of the Moore bound, the primary uncertainty in producing any particular Moore graph is the determination of tailend connections. We seek to construct the Moore bound, prove the existence of specific values of d and k, and describe and utilize a method to calculate the tail-end connections of these graphs
Research Sponsor
Dr. James Cossey
First Reader
Dr. Jeffrey Riedl
Second Reader
Dr. Stefan Forcey
Honors Faculty Advisor
Dr. Curtis Clemons
Proprietary and/or Confidential Information
No
Recommended Citation
Saxton, trevor, "Moore graphs" (2025). Williams Honors College, Honors Research Projects. 1993.
https://ideaexchange.uakron.edu/honors_research_projects/1993
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons