Hamiltonicity in directed toeplitz graphs of maximum (out or in)degree 4

Abstract

A directed Toeplitz graph is a digraph with a Toeplitz adjacency matrix. In this paper we study the hamiltonicity of the Toeplitz graphs of type T _n(1, 3, 4; t). For t ⋯ {2, 3, 4, 5, 8, 9}, we give conditions (on n) under which such a graph is hamiltonian. For t ⋯ {6, 7} and t ≥ 10, we see that T_n(1,3,4; t) is hamiltonian for all n.