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geodetic graphs; connected graph; shortest paths

References:

[1] M. Behzad G. Chartrand, L. Lesniak-Foster: **Graphs & Digraphs**. Prindle, Weber & Schmidt, Boston, 1979. MR 0525578

[2] D.C. Kay, G. Chartrand: **A characterization of certain ptolemaic graphs**. Canad. J. Math. 17 (1965), 342-346. DOI 10.4153/CJM-1965-034-0 | MR 0175113 | Zbl 0139.17301

[3] H.M. Mulder: **The Interval Function of a Graph**. Mathematisch Centrum, Amsterdam, 1980. MR 0605838 | Zbl 0446.05039

[4] L. Nebeský: **Route systems and bipartite graphs**. Czechoslovak Math. Journal 41 (116) (1991), 260-264. MR 1105440