Construction of uniquely vertex k-colorable graphs with minimum possible size
It was shown that a uniquely vertex k-colorable graph of order n has minimum size n(k - 1) - (2k), and a uniquely vertex 3-colorable extremal graph with the minimum degree 3 can be constructed. In this note, we construct an infinite family of uniquely vertex k-colorable graphs of the order n, the size n(k - 1) - (2k) and the minimum degree k by using a recursion method.
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