Graph theory in modern engineering : computer aided design, control, optimization, reliability analysis / Ernest J. Henley and R.A. Williams.

Contract no. N0014-68-A-0151 of the Office of Naval Research.

Includes bibliographical references (pages 295-296) and index.

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Front Cover; Graph Theory in Modern Engineering; Copyright Page; Contents; Preface; Acknowledgments; Nomenclature; Chapter 1. Basic Concepts; Directed Graphs; Flow Graphs for Differential Equations; Further Terminology; Chapter 2. Construction and Analysis of Signal Flow Graphs; Signal-Flow-Graph Reduction and the Solution of Equations; Flow-Graph Algebra; Loop Elimination and Equation Solving by Equation Reduction; Mason's Rule; Applying Mason's Rule; Application of Mason's Rule to Dynamic Systems; References; Chapter 3. Systematic Analysis of Large Flow Graphs

Determining Specific Paths and LoopsDetermining Specific Paths; List Processing Approach to Determining Paths; Evaluation of Gains; Removing Unnecessary Paths from the List Structure; Evaluating Determinants in Mason's Formula; Computing the Determinants Corresponding to Specific Paths as Required by Mason's Rule; Computing Transmittances; Implementing the Algorithms; References; Chapter 4. Frequency Response Analysis; Final Value Theorem; Initial Value Theorem; Substitution Rule; Bode Diagrams; A Typical Application; Other Stability Criteria; Reference; Chapter 5. Sensitivity Analysis

Sensitivity Analysis in GeneralDerivation of Network Functions; Deriving Sensitivity Functions; Applying Sensitivity Functions to Structural Analysis; Gain and Phase Sensitivity; Pole and Zero Sensitivity; Sensitivities via Structural Methods; Sensitivities for Large Parameter Variations; Transfer Functions and Sensitivities in Static Systems; References; Chapter 6. Examples and Further Applications; Closed-Form Solution of an Absorption Column; Sensitivity Analysis of a Heat Exchanger Network; Continuous Stirred Tank Reactor; Eigenvalue Problems; Ordering Recycle Calculations

Transportation ProblemsReferences; Chapter 7. Linear and Nonlinear Programming; General Form of LP Problems; Simplex Solution by Signal-Flow-Graph Methods; Example Problems; Discussion of Solution Procedure (MASNLP); An Advantage of MASNLP; Dual Simplex Method; Postoptimal Analysis; Sensitivity Analysis; Nonlinear Systems; Method of Feasible Directions; A Heat Exchanger Problem; Solution to the Heat Exchanger System; Results and Discussion; References; Chapter 8. Ranking by Flow-Graph Methods; Tennis Rankings; Implementation Difficulties; A Solution to the Implementation Problem; Reference

Chapter 9. Undirected GraphsUndirected Graphs; Trees; Logic Trees; Branch and Bound Methods; Trees-Further Theorems and Definitions; Disconnecting Sets and Cut-Sets; Bipartite Graphs; Assigning Output Sets; References; Chapter 10. Matrix Representation of Graphs; Nondirected Graphs; Digraphs; References; Chapter 11. Branch and Eound. Search Tree Methods; Formal Definition of the Branch and Bound Technique; The Traveling Salesman Problem; Integer Programming and Pseudo-Boolean Progrhmming; Generalization of the Branch and Bound Method; Bidding Contest Problem; Conclusion; References

Graph theory in modern engineering; computer aided design, control, optimization, reliability analysis.

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