The endomorphism monoids of (n − 3)-regular graphs of order n

Abstract

© Journal “Algebra and Discrete Mathematics”. This paper is motivated by the result of W. Li, that presents an infinite family of graphs - complements of cycles— which possess a regular monoid. We show that these regular monoids are completely regular. Furthermore, we characterize the regular, orthodox and completely regular endomorphisms of the join of complements of cycles, i.e. (n − 3)-regular graphs of order n.