​​​​​​​​Geodesic Convexity in Graphs is dedicated to the examine of the geodesic convexity on finite, basic, attached graphs. the 1st bankruptcy contains the most definitions and effects on graph idea, metric graph conception and graph course convexities. the subsequent chapters concentration completely at the geodesic convexity, together with motivation and heritage, particular definitions, dialogue and examples, effects, proofs, routines and open difficulties. the most and so much st​udied parameters related to geodesic convexity in graphs are either the geodetic and the hull quantity that are outlined because the cardinality of minimal geodetic and hull set, respectively. this article experiences a variety of effects, bought over the last one and a part decade, concerning those  invariants and a few others reminiscent of convexity quantity, Steiner quantity, geodetic new release quantity, Helly quantity, and Caratheodory quantity to a variety a contexts, together with items, boundary-type vertex units, and excellent graph households. This monograph can function a complement to a half-semester graduate course in geodesic convexity but is primarily a advisor for postgraduates and researchers drawn to subject matters with regards to metric graph thought and graph convexity idea.  ​

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