Hamltonian Connectedness and Toeplitz Graphs
A square matrix of order n is called Toeplitz matrix if it has constant elements along all diagonals parallel to the main diagonal and a graph is called Toeplitz graph if its adjacency matrix is Toeplitz. In this paper we proved that the Toeplitz graphs , for and are Hamiltonian connected.
R. Van Dal, G. Tijssen, Z. Tuza, J. A. A. Van Der Veen, Zamfirexcu, T. Zamfirescu, “Hamiltonian properties of Toeplitz graphs”, Discrete Mathe- matics 159, 69–81 (1996).
R. Euler, “Characterizing bipartite Toeplitz graphs”. Theor. Comput. Sci. 263, 47–58 (2001).
R. Euler, H. Leverge, T. Zamfirescu, “A characterization of infinite, bipartite Toeplitz graphs”. In: Tung-Hsin, K. (ed.) Combinatorics and Graph Theory 95, Vol. 1. Academia Sinica, pp. 119–130. World Scientific, Sin- gapore (1995).
R. Euler, T. Zamfirescu, “On planar Toeplitz graphs”. Graphs Comb. 29, 13111327 (2013).
C. Heuberger, “On Hamiltonian Toeplitz graphs”. Discret. Math. 245, 107– 125 (2002).
S. Malik, “Hamiltonicity in directed Toeplitz graphs of maximum (out or in) degree 4”. Util. Math. 89, 33–68 (2012)
S. Malik, A. M. Qureshi, “Hamiltonian cycles in directed Toeplitz graphs”. Ars Comb. 109, 511– 526 (2013).
S. Malik, T. Zamfirescu, “Hamiltonian connectedness in directed Toeplitz graphs”. Bull. Math. Soc. Sci. Math. Roum. 53 (101) No. 2, 145156 (2010).
M. F. Nadeem, A. Shabbir, T. Zamfirescu, “Hamiltonian Connectedness of Toeplitz Graphs”. Springer Basel 2015 P. Cartier et al. (eds.), Mathematics in the 21st Century, Springer Proceedings in Mathematics & Statistics 98, DOI 10.1007/978-3-0348-0859-08.
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