Overview
\u200b\u200b\u200b\u200b\u200b\u200b\u200b\u200bGeodesic Convexity in Graphs\xa0is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most st\u200budied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two \xa0invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester graduate\xa0course in geodesic convexity\xa0but is primarily\xa0a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory. \xa0\u200b
