On the Unitary Cayley Graph of a Finite Ring

  • Reza Akhtar
  • Megan Boggess
  • Tiffany Jackson-Henderson
  • Isidora JimĂ©nez
  • Rachel Karpman
  • Amanda Kinzel
  • Dan Pritikin

Abstract

We study the unitary Cayley graph associated to an arbitrary finite ring, determining precisely its diameter, girth, eigenvalues, vertex and edge connectivity, and vertex and edge chromatic number. We also compute its automorphism group, settling a question of Klotz and Sander. In addition, we classify all planar graphs and perfect graphs within this class.

Published
2009-09-18
Article Number
R117