Distance-hereditary graphs

Distance-hereditary graphs (sensu Howorka) are connected graphs in which all induced paths are isometric. Examples of such graphs are provided by complete multipartite graphs and ptolemaic graphs. Every finite distance-hereditary graph is obtained from K₁ by iterating the following two operations: adding pendant vertices and splitting vertices. Moreover, distance-hereditary graphs are characterized in terms of the distance function d, or via forbidden isometric subgraphs.