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Abstract: A Generalization of Geodetic Graphs: K-Geodetic Graphs

An undirected graph $G = (V,E)$ is said to be geodetic, if between any pair of vertices $x , y \in V$ there is a unique shortest path. Generalizations of geodetic graphs are introduced in this paper. K-geodetic graphs are defined as graphs in which every pair of vertices has at most k paths of minimum length between them. Some properties and characterizations of k--geod etic graphs are studied.