Geodetic blocks of diameter three
A graph is said to be geodetic if any two vertices are joined by a unique shortest path. The authors show that every geodetic block G of diameter 3 is self-centred (i.e. every vertex has eccentricity 3), upper and lower geodetic critical (i.e. \(G+e\) and G-e \((G\neq C_ 7)\) are not geodetic graphs) and lower diameter critical (i.e. \(diam(G-e)>3\)). Also further results are given.
scientific article; zbMATH DE number 3882472