A complete classification of perfect unitary Cayley graphs
J\'an Min\'a\v{c}, Tung T. Nguyen, Nguyen Duy T\^an
TL;DR
This paper provides a comprehensive classification of perfect unitary Cayley graphs derived from finite rings, connecting graph theory with algebra and number theory.
Contribution
It offers the first complete classification of perfect unitary Cayley graphs associated with finite rings, advancing understanding in algebraic graph theory.
Findings
Complete classification of perfect unitary Cayley graphs
Connections established between graph perfectness and algebraic structures
Enhanced understanding of the interplay between graph theory and finite rings
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.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph theory and applications · Advanced Graph Theory Research