Graph Theory Applications

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Springer Science & Business Media, Jan 20, 1995 - Mathematics - 408 pages
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Over the last 30 years graph theory has evolved into an important math ematical tool in the solution of a wide variety of problems in many areas of society. The purpose of this book is to present selected topics from this theory that have been found useful and to point out various applications. Some important theoretical topics have been omitted as they are not es sential for the applications in Part II. Hence Part I should not be seen as a well-rounded treatise on the theory of graphs. Some effort has been made to present new applications that do not use merely the notation and ter minology of graphs but do actually implement some mathematical results from graph theory. It has been written for final undergraduate year or first year graduate students in engineering, mathematics, computer science, and operations research, as well as researchers and practitioners with an inter est in graph theoretic modelling. Suggested plans for the reading of the book by people with these interests are given later. The book comprises two parts. The first is a brief introduction to the mathematical theory of graphs. The second is a discussion on the applications of this material to some areas in the subjects previously mentioned. It is, of course, possi ble to read only the first part to attempt to gain an appreciation of the mathematical aspects of graph theory. However even the purest of mathe maticians is strongly recommended to delve seriously into the second part.
 

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Contents

BASIC IDEAS
3
CONNECTIVITY
17
TREES
27
TRAVERSABILITY
43
PLANARITY
53
MATRICES
75
DIGRAPHS
93
COVERINGS AND COLOURINGS
123
Applications
193
OPERATIONS RESEARCH
225
ELECTRICAL ENGINEERING
269
INDUSTRIAL ENGINEERING
291
SCIENCE
323
CIVIL ENGINEERING
343
Further Reading
361
Index
379

ALGORITHMS
145
MATROIDS
183

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Page 369 - Eades, P., Foulds, LR, and Giffin, J. (1982), "An efficient heuristic for identifying a maximum weight planar subgraph", in: Lecture Notes in Mathematics No.

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