Graph Theory: Flows Matrices

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Overview

Graph Theory: Flows, Matrices covers a number of topics in graph theory that are important in the major areas of application. It provides graph theoretic tools that can be readily and efficiently applied to problems in operational research, computer science, electrical engineering, and economics. Emphasizing didactic principles, the book derives theorems and proofs from a detailed analysis of the structure of graphs. The easy-to-follow algorithms can be readily converted to computer codes in high-level programming languages. Requiring knowledge of the basic concepts of graph theory and a familiarity with some simple results, the book also includes 100 exercises with solutions to help readers gain experience and 131 diagrams to aid in the understanding of concepts and proofs.

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Editorial Reviews

Booknews
A textbook for graduate and undergraduate students of mathematics, engineering, computer science, operational research, and economics. Assumes a knowledge of graph theory and its results such as could be obtained from Andrasfai's 1971 (translated 1977) Introductory graph theory. Translated from the Hungarian edition (no date). Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780852742228
  • Publisher: CRC Press
  • Publication date: 1/28/1991
  • Pages: 280
  • Product dimensions: 6.50 (w) x 9.50 (h) x 1.00 (d)

Table of Contents

STRUCTURE OF THE GRAPH MODEL
The abstract graph
Geometrical realization of graphs
Components
Leaves
Blocks
The strongly connected components of directed graphs
Problems

OPTIMAL FLOWS
Two basic problems
Maximal set of independent paths
The optimal assignment problem
The Hungarian method
Max flow-min cut
Dynamic flow
The mobilization problem
The synthesis of flow problems
Optical planning
The role of the critical path
Minimal cost transportation
Minimal cost flows
Problems

GRAPHS AND MATRICES
The adjacency matrix
The incidence matrix
The circuit matrix
Interrelations between the matrices of graphs
The spectrum of graphs, the complexity
Linear electrical networks
Further matrices associated with graphs
Problems and solutions

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