Geodesic Convexity in Graphs

1. Front Matter

   Pages i-viii

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2. Introduction

   • Ignacio M. Pelayo

   Pages 1-8

3. Invariants

   • Ignacio M. Pelayo

   Pages 9-38

4. Graph Operations

   • Ignacio M. Pelayo

   Pages 39-56

5. Boundary Sets

   • Ignacio M. Pelayo

   Pages 57-68

6. Steiner Trees

   • Ignacio M. Pelayo

   Pages 69-79

7. Oriented Graphs

   • Ignacio M. Pelayo

   Pages 81-90

8. Computational Complexity

   • Ignacio M. Pelayo

   Pages 91-93

9. Back Matter

   Pages 95-112

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​​​​​​​​Geodesic Convexity in Graphs is 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​udied 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  invariants 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 course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory.  ​

• Convex hull
• Geodesic convexity
• Geodetic closure
• Graph convexity
• Hull set
• Metric graph theory
• partial differential equations

• School of Agricultural Engineering of Barcelona, Barcelona, Spain

  Ignacio M. Pelayo

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