The open geodetic number of a graph

Abstract

One concept that pervades all of graph theory is that newlineof distance, and distance is used in isomorphism testing, graph operations, hamil- newlinetonicity problems, extremal problems on connectivity and diameter, and convexity newlinein graphs. The distance d(u, v) between two vertices u and v in a connected graph newlineG is defined to be the length of a shortest u-v path in G. This gives rise to the newlineconcepts of geodetic set, geodetic number, open geodetic set, open geodetic num- newlineber, connected open geodetic set and connected open geodetic number of a graph newline[1, 2, 4, 5, 6, 7, 8, 9, 12, 13]. Graph theory, as such, has tremendous applications newlinein theoretical Chemistry. Distance concepts in graphs, in particular, the graph in- newlinevariants arising from various distance are widely applied in Chemical graph theory. newlineGeodetic concepts have many applications in location theory and convexity theory. newline