Shabnam Malik, Ahmad Mahmood Qureshi: Hamiltonicity in directed Toeplitz graphs $T_n\langle 1, 3, 5; t\rangle$, 239-252

Abstract:

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 (a square matrix that has constant values along all diagonals parallel to the main diagonal). In this paper, we study hamiltonicity in directed Toeplitz graphs $T_n\langle 1, 3, 5; t\rangle$.

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

2020 Mathematics Subject Classification: Primary 05C20; Secondary 05C45.

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