National Taiwan University Dept MathChang, Gerard-J.Gerard-J.ChangTong, Li-DaLi-DaTongWang, Hong-TsuHong-TsuWang2006-11-152018-06-282006-11-152018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/2006111501265209Geodetic numbers of graphs & digraphs have been investigated in the literature recently. The main purpose of this paper is to study the geodetic spectrum of a graph. For any two vertices u & v in an oriented graph D, a u–v geodesic is a shortest directed path from u to v. Let I (u, v) denote the set of all vertices lying on a u–v geodesic. For a vertex subset A, let I (A) denote the union of all I (u, v) for u, v ∈ A. The geodetic number g(D) of an oriented graph D is the minimum cardinality of a set A with I (A) = V(D). The (strong) geodetic spectrum of a graph G is the set of geodetic numbers of all (strongly connected) orientations of G. In this paper, we determine geodetic spectra & strong geodetic spectra of several classes of graphs. A conjecture & two problems given by Chartrand & Zhang are dealt with.application/pdf195659 bytesapplication/pdfzh-TWConvex setGeodesicGeodetic numberGeodetic spectrumConnected graphComplete graphCycleTreeComplete r-partite graphjournal articlehttp://ntur.lib.ntu.edu.tw/bitstream/246246/2006111501265209/1/5611.pdf