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About: Geodetic graph

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In graph theory, a geodetic graph is an undirected graph such that there exists a unique (unweighted) shortest path between each two vertices. Geodetic graphs were introduced in 1962 by Øystein Ore, who observed that they generalize a property of trees (in which there exists a unique path between each two vertices regardless of distance), and asked for a characterization of them. Although these graphs can be recognized in polynomial time, "more than sixty years later a full characterization is still elusive".

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  • In graph theory, a geodetic graph is an undirected graph such that there exists a unique (unweighted) shortest path between each two vertices. Geodetic graphs were introduced in 1962 by Øystein Ore, who observed that they generalize a property of trees (in which there exists a unique path between each two vertices regardless of distance), and asked for a characterization of them. Although these graphs can be recognized in polynomial time, "more than sixty years later a full characterization is still elusive". (en)
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  • In graph theory, a geodetic graph is an undirected graph such that there exists a unique (unweighted) shortest path between each two vertices. Geodetic graphs were introduced in 1962 by Øystein Ore, who observed that they generalize a property of trees (in which there exists a unique path between each two vertices regardless of distance), and asked for a characterization of them. Although these graphs can be recognized in polynomial time, "more than sixty years later a full characterization is still elusive". (en)
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  • Geodetic graph (en)
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