On the endomorphism monoid of K(n, 4)

Abstract

In this paper, the endomorphism monoid of circulant complete graph K(n,3) is explored explicitly. It is shown that AutK(n,3)) =Dn, the dihedral group of degree n. It is also shown that K(n,3) is unretractive when 3 does not divide n, End(K(3m,3)) =qEnd(K(3m,3)), sEnd(K(3m,3)) =Aut(K(3m,3)) and K(3m,3) is endomorphism-regular. The structure of End(K(3m,3)) is characterized and some enumerative problems concerning End(K(n,3)) are solved.