Geodesic convexity in graphs [electronic resource] /
Pelayo, Ignacio M.author.
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.  .
Description based upon print version of record.
Preface; Contents; Chapter1 Introduction; 1.1 Graph Theory; 1.2 Metric Graph Theory; 1.3 Convexity Spaces; 1.4 Graph Convexities; Chapter2 Invariants; 2.1 Geodetic Closure and Convex Hull; 2.2 Geodetic and Hull Numbers; 2.3 Monophonic and m-Hull Numbers; 2.4 Convexity Number; 2.5 Forcing Geodomination; 2.6 Closed Geodomination; 2.7 Geodetic Domination; 2.8 k-Geodomination; 2.9 Edge Geodomination; 2.10 Classical Parameters; Chapter3 Graph Operations; 3.1 Cartesian Product; 3.2 Strong Product; 3.3 Lexicographic Product; 3.4 Join; 3.5 Corona Product; Chapter4 Boundary Sets
Chapter5 Steiner TreesChapter6 Oriented Graphs; Chapter7 Computational Complexity; Glossary; References; Index; Symbol Index
Includes bibliographical references and index.
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.  .
Graph theory.
Differential geometry.
Partial differential equations.
Graph Theory.
Differential Geometry.
Partial Differential Equations.