On Diameters and Radii of Bridged Graphs.

A subgraph H of a graph G is isometric if the distance between any pair of vertices in H is the same as that in G, and is induced if two vertices of H are adjacent in H whenever they are adjacent in G. A graph is bridged if it contains no isometric cycles of length greater than 3. The class of bridged graphs is a natural extension of the well-studied class of chordal (or triangulated) graphs, which consists of all graphs containing no induced cycles of length greater than 3. In this paper we investigate certain metric properties of bridged graphs. In particular, we study the relationship between the radius and diameter of a bridged graph.