14 research outputs found
Characterization of finite simple semigroup digraphs
This paper characterizes directed graphs which are Cayley graphs of finite simple semigroups, i.e. of a subspecies of completely regular semigroups. Moreover we investigate the structure of Cayley graphs of finite simple semigroups with a one-element connection set. We introduce the conditions for which they are isomorphic and connected
Endomorphisms of Cayley digraphs of rectangular groups
Let Cay(S,A) denote the Cayley digraph of the semigroup S with respect to the set A, where A is any subset of S. The function f : Cay(S,A) β Cay(S,A) is called an endomorphism of Cay(S,A) if for each (x, y) β E(Cay(S,A)) implies (f(x), f(y)) β E(Cay(S,A)) as well, where E(Cay(S,A)) is an arc set of Cay(S,A). We characterize the endomorphisms of Cayley digraphs of rectangular groups G Γ L Γ R, where the connection sets are in the form of A = K Γ P Γ T
The endomorphisms monoids of graphs of order n with a minimum degree n β 3
We characterize the endomorphism monoids, End(G), of the generalized graphs G of order n with a minimum degree n β 3. Criteria for regularity, orthodoxy and complete regularity of those monoids based on the structure of G are given
The Endomorphism Monoids of (n β 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. (nβ3)-regular graph of order n