On the chromatic number of Toeplitz graphs

Let $n, a_1, a_2, . . . , a_k$ be distinct positive integers. A finite Toeplitz graph $T_n(a_1, a_2, . . . , a_k) = (V, E)$ is a graph where $V = {v_0, v_1, . . . , v_{n-1}}$ and $E = {(v_i,v_j), for |i-j| ? {a_1, a_2, . . . , a_k}}$. In this paper, we first refine some previous results on the connectivity of finite Toeplitz graphs with $k = 2$, and then focus on Toeplitz graphs with $k = 3$, proving some results about their chromatic number.