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Further Applications of Schur Rings to Produce GRRs for Dihedral Groups

Jonathan Ebejer, Josef Lauri

Abstract

This note is a continuation of postgraduate thesis research carried out by the first author under the supervision of the second author at the University of Malta. In that research we took a look at several results relating Schur rings to sufficient conditions for GRRs and then applied those results to produce numerical methods for constructing trivalent GRRs for dihedral groups very quickly.

Further Applications of Schur Rings to Produce GRRs for Dihedral Groups

Abstract

This note is a continuation of postgraduate thesis research carried out by the first author under the supervision of the second author at the University of Malta. In that research we took a look at several results relating Schur rings to sufficient conditions for GRRs and then applied those results to produce numerical methods for constructing trivalent GRRs for dihedral groups very quickly.
Paper Structure (2 sections, 6 theorems, 4 equations)

This paper contains 2 sections, 6 theorems, 4 equations.

Table of Contents

  1. Foundations
  2. Main Results

Key Result

Theorem 1.0.1

$\hbox{Aut}(\hbox{Cay}(\Gamma,C))=\hbox{Aut}(\langle\langle C \rangle\rangle )$MuPo

Theorems & Definitions (9)

  • Definition 1.0.1: Cayley graphs
  • Theorem 1.0.1
  • Theorem 1.0.2
  • Theorem 1.0.3: Schur-Wielandt Principle
  • Theorem 1.1
  • Lemma 1.1
  • proof
  • Lemma 1.2
  • proof