The codiameter of a 2-connected graph Original Research Article

The codiameter of a graph is defined as the minimum, taken over all pairs of vertices u and image in the graph, of the maximum length of a image-path. A result of Fan [Long cycles and the codiameter of a graph, I, J. Combin. Theory Ser. B 49 (1990) 151–180.] is that, for an integer image, if G is a 2-connected graph on n vertices with more than image edges, the codiameter of G is at least c. The result is best possible when image is divisible by image. In this paper, we shall show that the bound image can be decreased when image is not divisible by image.