Geodesic Convexity in Graphs

Ignacio M. Pelayo

ISBN 10: 146148698X / ISBN 13: 9781461486985

Published by Springer New York Sep 2013, 2013

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 120 pp. Englisch.

Seller Inventory # 9781461486985

Bibliographic Details

• Title: Geodesic Convexity in Graphs
• Publisher: Springer New York Sep 2013
• Publication Date: 2013
• Language: English
• ISBN 10: 146148698X
• ISBN 13: 9781461486985
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 7D millimeters 235 millimeters width by 155 millimeters height by 7 millimeters depth
• Weight: 195 grams

About this title

Synopsis

​​​​​​​​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.  ​