Graph theory applications
著者
書誌事項
Graph theory applications
（Universitext）
Springer-Verlag, c1992
- : New York
- : Berlin
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注記
Corrected 2nd printing (1994) paged as: xv p.
Some printing without "corrected 2nd printing" paged as: xv p.
Bibliography: p. 365-378
Includes index
内容説明・目次
- 巻冊次
-
: New York ISBN 9780387975993
内容説明
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.
目次
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.
- 巻冊次
-
: Berlin ISBN 9783540975991
内容説明
This text offers an upper undergraduate or first year graduate level introduction to the theory of graphs and its application in engineering and science. The first part covers the main graph theoretic topics: connectivity, trees, transversability, planarity, colouring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms and matroids. In the second part, these concepts are applied to problems in engineering, operations research and science as well as to an interesting set of miscellaneous problems, illustrating the broad applicability of the subject. Some effort has been made to present applications that use not only the notation and terminology of graph theory but also the actual mathematical result of the subject. Some of the applications, such as molecular evolution, facilities layout and traffic network design have not appeared in book form before. The book is suitable for students of mathematics, engineering, operations research, computer science and physical science as well as researchers and practitioners with an interest in graph theoretic modelling.
目次
1: Basic Ideas. 2: Connectivity. 3: Trees. 4: Traversability. 4: Planarity. 6: Matrices. 7: Digraphs. 8: Coverings and Colourings. 9: Algorithms. 10: Matroids. 11: Miscellaneous Applications. 12: Operations Research. 13: Electrical Engineering. 14: Industrial Engineering. 15: Science. 16: Civil Engineering.
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