On uniquely 3-colorable graphs II

In [2], for each non-negative integer k, we constructed a connected graph with (24)2k vertices which is uniquely 3-colorable, regular with degree k + 5, and triangle-free. Here, for each positive integer n and each integer r ⩾ 5, we construct a connected graph with (26)n · 2r−5 vertices which is uniquely 3-colorable, regular with degree r, and triangle-free.