Journal of Prime Research in Mathematics
Vol. 20 (2024), Issue 2, pp. 64 – 76
ISSN: 1817-3462E (Online) 1818-5495 (Print)
ISSN: 1817-3462E (Online) 1818-5495 (Print)
Hamiltonicity in directed Toeplitz graphs having increasing edges of length 1, 3 and 7
Shabnam Malik\(^{a,∗}\), Farzaneh Ramezani\(^b\)
\(^a\)Faculty of Mathematics, Forman Christian College (A Chartered University) Lahore, Pakistan.
\(^b\)Faculty of Mathematics, K.N. Toosi University of Technology P.O. Box 16765-3381, Tehran, Iran.
Correspondence should be addressed to: shabnam.malik@gmail.com , ramezani@kntu.ac.ir
Copyright © 2024 Shabnam Malik, Farzaneh Ramezani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: Received: 07 August 2024 Accepted: 27 October 2024; Published Online: 29 October 2024
Abstract
A directed Toeplitz graph Tn⟨a1, . . . , ap; b1, . . . , bq⟩ with vertices 1, 2, . . . , n, where the edge (i, j) occurs if and only if j − i = as or i − j = bt for some 1 ≤ s ≤ p and 1 ≤ t ≤ q, is a digraph whose adjacency matrix is a Toeplitz matrix. In this paper, we study hamiltonicity in directed Toeplitz graphs having increasing edges of length 1, 3 and 7, only.
Keywords:
Adjacency matrix; Toeplitz graph; Hamiltonian graph.