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connected graph; induced path; ternary relation; finite structure

References:

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[6] H. M. Mulder: **The interval function of a graph**. MC-tract 132, Mathematisch Centrum, Amsterdam, 1980. MR 0605838 | Zbl 0446.05039

[7] H. M. Mulder: **Transit functions on graphs**. In preparation. Zbl 1166.05019

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[12] L. Nebeský: **The interval function of a connected graph and a characterization of geodetic graphs**. Math. Bohem. 126 (2001), 247–254. MR 1826487 | Zbl 0977.05045