Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2012 On highly regular digraphs Oktay Olmez Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Mathematics Commons Recommended Citation Olmez, Oktay, "On highly regular digraphs" (2012). Graduate Theses and Dissertations. 12626. https://lib.dr.iastate.edu/etd/12626 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact
[email protected]. On highly regular digraphs by Oktay Olmez A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Mathematics Program of Study Committee: Sung Yell Song, Major Professor Maria Axenovich Clifford Bergman L. Steven Hou Paul Sacks Iowa State University Ames, Iowa 2012 Copyright c Oktay Olmez, 2012. All rights reserved. ii DEDICATION I would like to dedicate this thesis to my wife, Sevim, without whose support I would not have been able to complete this work. I would also like to thank my friends and family for their loving guidance during the writing of this work. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS . v ABSTRACT . vi CHAPTER 1. GENERAL OVERVIEW AND INTRODUCTION . 1 CHAPTER 2. PREMINILARIES . 4 2.1 Finite Incidence Structures . .4 2.2 Difference Sets . .7 1 2.3 1 2 -Designs . .9 2.4 Association Schemes .