#### Title

On highly regular digraphs

Dissertation

2012

#### Degree Name

Doctor of Philosophy

Mathematics

Sung Song

#### Abstract

We explore directed strongly regular graphs (DSRGs) and their connections to association schemes and finite incidence structures. More specically, we study flags and antiflags of finite

incidence structures to provide explicit constructions of DSRGs. By using this connection between the finite incidence structures and digraphs, we verify the existence and non-existence of $1\frac{1}{2}$-designs with certain parameters by the existence and non-existence of corresponding digraphs, and vice versa. We also classify DSRGs of given parameters according to isomorphism classes. Particularly, we examine the actions of automorphism groups to provide explicit

examples of isomorphism classes and connection to association schemes. We provide infinite families of vertex-transitive DSRGs in connection to non-commutative association schemes.

These graphs are obtained from tactical configurations and coset graphs.

#### DOI

https://doi.org/10.31274/etd-180810-226

Oktay Olmez

en

application/pdf

85 pages

COinS