Let n, a_1, a_2, . . ., ak 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_iv_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.
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