On the chromatic number of Toeplitz graphs

Let n, a1, a2, . . . , ak be distinct positive integers. A finite Toeplitz graph Tn(a1, a2, . . . , ak) = (V, E) is a graph where V = {v0, v1, . . . , vn-1} and E = {vivj, for |i-j| ? {a1, a2, . . . , ak}}. 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.