Graph Theory: Flows, Matrices, 1st Edition (Hardback) book cover

Graph Theory

Flows, Matrices, 1st Edition

By B Andrasfai

CRC Press

280 pages

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Hardback: 9780852742228
pub: 1991-01-01
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Description

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.

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

Subject Categories

BISAC Subject Codes/Headings:
MAT036000
MATHEMATICS / Combinatorics