Most finite distance-transitive graphs with diameter over 4 are geodesic-transitive apart from few exceptions, with new examples of distance-transitive but not geodesic-transitive graphs and explicit geodesics for polar Grassmann graphs.
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Geodesic-transitive graphs with large diameter
Most finite distance-transitive graphs with diameter over 4 are geodesic-transitive apart from few exceptions, with new examples of distance-transitive but not geodesic-transitive graphs and explicit geodesics for polar Grassmann graphs.