Graph families

Geodetic graph

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". (Wikipedia).

Geodetic graph
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Planar graph | Cactus graph | Homeomorphism (graph theory) | Degree (graph theory) | Tree (graph theory) | Clique problem | Clique (graph theory) | Block graph | Cycle graph | Levi graph | Complete graph | Øystein Ore | Diamond graph | Biconnected component | Windmill graph | Petersen graph | Affine plane (incidence geometry) | Strongly regular graph | Hoffman–Singleton graph