Document Type : Original Article

Authors

• Jan Minac ¹
• Tung T. Nguyen ²
• Duy Tan Nguyen ³

¹ Department of Mathematics, Western University, London, Ontario, Canada N6A 5B7

² Department of Kinesiology, Western University, London, Ontario, Canada N6A 5B7

³ Faculty of Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

Abstract

Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra, representation theory, and graph theory. In this article, we study the perfectness property of these graphs. More precisely, we provide a complete classification of perfect unitary Cayley graphs associated with finite rings.

Keywords

• Cayley graphs
•  Perfect graphs
• Finite semisimple rings

Main Subjects

• Algebraic graph theory (MSC 05C)