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On Kotzig's conjecture concerning graphs with a unique regular path-connectivity☆
Discrete Mathematics 211(2000)287-298，-0001，（）：
Kotzig (see Bondy and Murty, Graph Theory with Applications, North-Holland, Amsterdam, 1976) conjectured that there exists no graph with the property that every pair of vertices is connected by a unique path of length k, k>2. Kotzig (Graph Theory and Related Topics, Academic Press, New York, 1979, pp. 358-367) has proved this conjecture for 2<k<9. Xing and Hu (Discrete Math. 135 (1994) 387-393) have proved it for k>11. Here we prove this conjecture for the remaining cases k=9, 10, 11.
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