Hamiltonicity in Directed Toeplitz Graphs with s 1 = 1 and s 3 = 4

Abstract

A directed Toeplitz graph $T_n〈s_1,\cdots ,s_k;t_1,\cdots ,t_l〉$ with vertices $1$ , $2$ , $\cdots$ , $n$ is a directed graph whose adjacency matrix is a Toeplitz matrix. In this paper, we investigate the Hamiltonicity in directed Toeplitz graphs $T_n〈s_1,\cdots ,s_k;t_1,\cdots ,t_l〉$ with $s_1=1$ and $s_3=4$ .