Digraph of the full transformation semigroup

Abstract

Let X_n = {1,2, … ,n} be a finite set. A (partial) transformation α is said to be full if the whole of X_n is the domain which is given as Dom(a) = X_n. A digraph of the transformation Γ_α is naturally created.

In this paper, we characterize the number of strongly connected, strictly unilaterally connected, strictly weakly connected, Hamiltonian, Eulerian and self-converse digraph of the full transformation semigroup.

Subject Classification:

• 20M20
• 05C30

Keywords:

• Digraph
• Digraph of transformation
• Full transformation semigroup
• Connectedness
• Hamiltonian and Eulerian digraph
• Self-converse digraphs