Hamiltonian Cycles in Directed Toeplitz Graphs

Abstract

An $(n\times n)$ matrix $A=(a_{ij})$ is called a Toeplitz matrix
if it has constant values along all diagonals parallel to the main diagonal.
A directed Toeplitz graph is a digraph with Toeplitz adjacency matrix.
In this paper, we discuss conditions for the existence of Hamiltonian cycles
in directed Toeplitz graphs.