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Graph theoretical problems based on shortest paths are at the core ofresearch due to their theoretical importance and applicability. This paperdeals with the geodetic number which is a global measure for simple connectedgraphs and it belongs to the path covering problems: what is theminimal-cardinality set of vertices, such that all shortest paths between itselements cover every vertex of the graph. Inspired by the exact 0-1 integerlinear programming formalism from the recent literature, we propose a newmethods to obtain upper bounds for the geodetic number in an algorithmic way.The efficiency of these algorithms are demonstrated on a collection ofstructurally different graphs.

Algorithmic upper bounds for graph geodetic number