Graph Theory Applications - Brossura

Foulds, L.R.

Brossura

ISBN 10: 0387975993 ISBN 13: 9780387975993

Casa editrice: Springer, 2013

Riassunto

The first part of this text covers the main graph theoretic topics: connectivity, trees, traversability, planarity, colouring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids. These concepts are then applied in the second part to problems in engineering, operations research, and science as well as to an interesting set of miscellaneous problems, thus illustrating their broad applicability. Every effort has been made to present applications that use not merely the notation and terminology of graph theory, but also its actual mathematical results. Some of the applications, such as in molecular evolution, facilities layout, and graffic network design, have never appeared before in book form. Written at an advanced undergraduate to beginning graduate level, this book is suitable for students of mathematics, engineering, operations research, computer science, and physical sciences as well as for researchers and practitioners with an interest in graph theoretic modelling.

Su questo libro

Recensione

L.R. Foulds

Graph Theory Applications

"This book put[s] together the theory and applications of graphs in a single, self-contained, and easily readable volume . . . the fundamentals of graph theory are presented in a very accessible way . . . Each part is divided into chapters, each concluding with a summary and a nice collection of exercises . . . The book can serve as an excellent textbook for a course in graph theory either at the undergraduate or graduate level. It can also be used by researchers in application areas who use graph theory in their research or by pure graph theorists who want to know about the applications of their research."―ZENTRALBLATT MATH

Contenuti

I: The Theory of Graphs.- 1: Basic Ideas.- History.- Initial Concepts.- Summary.- Exercises.- 2: Connectivity.- Elementary Results.- Structure Based on Connectivity.- Summary.- Exercises.- 3: Trees.- Characterizations.- Theorems on Trees.- Tree Distances.- Binary Trees.- Tree Enumeration.- Spanning Trees.- Fundamental Cycles.- Summary.- Exercises.- 4: Traversability.- Eulerian Graphs.- Hamiltonian Graphs.- Summary.- Exercises.- 5: Planarity.- The Utilities Problem.- Plane and Planar Graphs.- Planar Graph Representation.- Planarity Detection.- Duality.- Thickness and Crossing Numbers.- Summary.- Exercises.- 6: Matrices.- The Adjacency Matrix.- The Incidence Matrix.- The Cycle Matrix.- The Cut-Set Matrix.- The Path Matrix.- Summary.- Exercises.- 7: Digraphs.- Connectivity.- Traversability.- Directed Trees.- More Digraph Matrices.- The Principle of Directional Duality.- Tournaments.- Summary.- Exercises.- 8: Coverings and Colourings.- Covering, Independence, and Domination.- Colouring.- Matching.- Summary.- Exercises.- 9: Algorithms.- Algorithms.- Input.- Complexity.- Output.- Graph Analysis Algorithms.- Graph Optimization Algorithms.- Summary.- Exercises.- 10: Matroids.- Duality.- The Greedy Algorithm.- Summary.- Exercises.- II: Applications.- 11: Miscellaneous Applications.- Social Sciences.- Economics.- Geography.- Architecture.- Puzzles and Games.- Summary.- Exercises.- 12: Operations Research.- Operations Research and Graph Theory.- Graph Theoretic Algorithms in OR.- Graph Theoretic Heuristics in OR.- Digraphs in OR.- Optimization Algorithms.- Transportation Networks: Advanced Models.- Summary.- Exercises.- 13: Electrical Engineering.- Electrical Network Analysis.- Printed Circuit Design.- Summary.- Exercises.- 14: Industrial Engineering.- Production Planning and Control.- Facilities Layout.- Summary.- Exercises.- 15: Science.- Physics.- Chemistry.- Biology.- Summary.- Exercises.- 16: Civil Engineering.- Earthwork projects.- Traffic Network Design.- Summary.- Exercises.- Further Reading.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2013
• ISBN 10: 0387975993
• ISBN 13: 9780387975993
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 408