Let $n,\,t_1,\,\ldots,\,t_k$ be distinct positive integers. A Toeplitz graph $G=(V, E)$ is a graph with $V =\{1,\ldots,n\}$ and $E= \{(i,j)\mid |i-j|\in \{t_1,\ldots,t_k\}\}$. In this paper, we present some results on decomposition of Toeplitz graphs.
R. van Dal, G. Tijssen, Z. Tuza, J. A. A. van der Veen, Ch. Zamfirescu and T. Zamfirescu (1996). Hamiltonian properties of Toeplitz graphs. Discrete Math.. 159, 69-81 R. Euler, H. Le Verge and T. Zamfirescu (1995). A characterization of infinite, bipartite Toeplitz graphs. Combinatorics and graph theory '95, World Sci. Publ., River Edge, NJ. 1, 119-130 R. Euler (November 1998). Coloring infinite, planar Toeplitz graphs. Tech. Report, Laboratoire d'Informatique de Brest (LIBr). R. Euler (2001). Characterizing bipartite Toeplitz graphs. Theoret. Comput. Sci.. 263, 47-58 C. Heuberger (2002). On Hamiltonian Toeplitz graphs. Discrete Math.. 245, 107-125 S. Malik and A. M. Qureshi Hamiltonian cycles in directed Toeplitz graphs. Ars Combinatoria, to appear.. S. Malik Hamiltonian cycles in directed Toeplitz graphs-- part 2. Ars Combinatoria, to appear.. S. Malik Hamiltonian in directed Toeplitz graphs of maximum (out or in) degree $4$. Utilitas Mathematica, to appear.. S. Malik and T. Zamfirescu (2010). Hamiltonian connectedness in directed Toeplitz graphs. Bull. Math. Soc. Sci. Math. Roumanie (N.S.). 53(101) (2), 145-156 S. Bau (2011). A generalization of the concept of Toeplitz graphs. Mong. Math. J.. 15, 45-61 R. Euler and T. Zamfirescu On planar Toeplitz graphs. Graphs and Combinatorics, to appear.. J. Petersen (1891). Die Theorie der regul"aren graphs. Acta Math.. 15, 193-220 O. Veblen (1912/13). An application of modular equations in analysis situs. Ann. of Math. (2). 14, 86-94 D. B. West (2001). Introduction to Graph Theory. second eddition, Prentice--Hall, New Jersey.
)