Hamiltonicity in directed Toeplitz graphs Tn1, 2;t1, t2

Abstract

A square matrix of order n is called a Toeplitz matrix if it has constant val- ues along all diagonals parallel to the main diagonal. A directed Toeplitz graph Tn⟨s1; : : : ; sk; t1; : : : ; tl⟩ with vertices 1; 2; : : : ; n, where the edge (i; j) occurs if and only if j − i = sp or i − j = tq for some 1 ≤ p ≤ k and 1 ≤ q ≤ l, is a digraph whose adjacency matrix is a Toeplitz matrix. In this paper, we study hamiltonicity in directed Toeplitz graphs Tn⟨1; 3; 1; t⟩. We obtain new results and improve existing results on Tn⟨1; 3; 1; t⟩.