The contour of a bridged graph is geodetic

The eccentricity of a vertex v in a graph G is the maximum distance of v from any other vertex of G and v is a contour vertex of G if each vertex adjacent to v has eccentricity not greater than the eccentricity of v. The set of contour vertices of G is geodetic if every vertex of G lies on a shortest path between a pair of contour vertices. An induced connected subgraph H of G is isometric if, every two vertices of H, have in H the same distance as in G. A graph is bridged if it does not contains an isometric cycle with length greater than 3. In this note, we show that the contour of a bridged graph is geodetic. © 2015 Elsevier B.V. All rights reserved.