The Endomorphism Monoids of (n − 3)-regular Graphs of Order n

This paper is motivated by the result of W. Li, he 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 graph of order n

The endomorphisms monoids of graphs of order n with a minimum degree n − 3

We characterize the endomorphism monoids, End(G), of the generalized graphs G of order n with a minimum degree n − 3. Criteria for regularity, orthodoxy and complete regularity of those monoids based on the structure of G are given

Cores and Compactness of Infinite Directed Graphs

AbstractIn this paper we define the property of homomorphic compactness for digraphs. We prove that if a digraphHis homomorphically compact thenHhas a core, although the converse does not hold. We also examine a weakened compactness condition and show that when this condition is assumed, compactness is equivalent to containing a core. We use this result to prove that if a digraphHof sizeκis not compact, then there is a digraphGof size at mostκ+such thatHis not compact with respect toG. We then give examples of some sufficient conditions for compactness