__Abstract__:
**A Generalization of Geodetic Graphs: K-Geodetic Graphs**

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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.
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