Shabnam Malik: Hamiltonicity in directed Toeplitz graphs $T_n\langle 1, 3; 1, t\rangle$, 307-318

Abstract:

A square matrix of order $n$ is called a Toeplitz matrix if it has constant values along all diagonals parallel to the main diagonal. A directed Toeplitz graph $T_n\langle s_1,\dots,s_k;t_1,\dots,t_l\rangle$ with vertices $1, 2, \dots, n$, where the edge $(i,\,j)$ occurs if and only if $j-i=s_p$ or $i-j=t_q$ for some $1\leq p\leq k$ and $1\leq q\leq l$, is a digraph whose adjacency matrix is a Toeplitz matrix. In this paper, we study hamiltonicity in directed Toeplitz graphs $T_n\langle 1, 3; 1, t\rangle$. We obtain new results and improve existing results on $T_n\langle 1, 3; 1, t\rangle$.

Key Words: Adjacency matrix, Toeplitz graph, Hamiltonian graph, length of an edge.

2010 Mathematics Subject Classification: Primary 05C20; Secondary 05C45.

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