摘要
Abstract It was shown that a uniquely vertex k-colorable graph of order n has minimum size n（k - 1） - （^k2）, and a uniquely vertex 3-colorable extremal graph with the minimum degree 3 can be constructed. In this note, we construct-an infinite familyof uniquely vertex k-colorable graphs of the order n, the size n（k - 1） - （^k2） and the minimum degree k by using a recursion method.
Abstract It was shown that a uniquely vertex k-colorable graph of order n has minimum size n（k - 1） - （^k2）, and a uniquely vertex 3-colorable extremal graph with the minimum degree 3 can be constructed. In this note, we construct-an infinite familyof uniquely vertex k-colorable graphs of the order n, the size n（k - 1） - （^k2） and the minimum degree k by using a recursion method.
基金
Project supported by the National Natural Science Foundation of China （Grant No.10101010）, and the Natural Science Development Foundation of Shanghai Municipal Commission of Education （Grant No.05AZ04）
