Abstract
Bigeodetic graphs, a generalization of geodetic and interval-regular graphs, are defined as graphs in which each pair of vertices has at most two paths of minimum length between them. The block cut-vertex incidence pattern of bigeodetic separable graphs are discussed. Two characterizations of bigeodetic graphs are given and some properties of these graphs are studied. Construction of planar bigeodetic blocks with given girth and diameter, and construction of hamiltonian and eulerian/nonhamiltonian and noneulerian, perfect bigeodetic blocks are discussed. The extremal bigeodetic graph of diameterd onp ? d + 1 vertices is constructed.
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