Abstract
Geodetic number of a graph is one of the widely studied graph theoretic parameters concerning geodesic convexity in graphs. In this paper, we introduce a variant of this parameter namely, doubly geodetic number of a graph. For a connected graph G, a setSof vertices of Gis called a doubly geodetic set ofGif each vertex inV − Slies on atleast two distinct geodesics of vertices in S.The doubly geodetic numberd g G of G is the minimum cardinality of a doubly geodetic set. Any doubly geodetic set of cardinality d g G is called d g-set of G. In this paper, the doubly geodetic number of certain standard graphs is determined.
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