Graph Dynamics

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CRC Press, Nov 22, 1995 - Mathematics - 248 pages
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Study of "graph operators" or "graph-valued functions" such as the line graph, the clique graph, the complement, and powers, raises several immediate questions: Which graphs are fixed under the operator? Which graphs appear as images of graphs? What happens if the operator is iterated? Over the last 30 years these questions have been answered and methods developed for particular operators in literally hundreds of papers on the subject. Nowhere, however, could one find a comprehensive treatment-a unification of terminology, questions, and methods.

Graph Dynamics provides that comprehensive treatment. Its purpose is threefold: it serves as an introductory textbook on the topic, offers an encyclopedic survey of the literature, and reports recent research-both new tools and results on concrete operators. Part I explicitly presents graph dynamics general theory, stating general principles illustrated by application to graph operators. Part 2 addresses the operators themselves. It lists all known graph operators grouped together in families and recounts, with complete references, all that is known about the dynamical behavior of these concrete operators.

Graph Dynamics is the book you need if you are looking for information on a particular operator, need a text for advanced students, or want to review collected research results presented with a common terminology. It is clearly an essential resource for anyone working in or studying algebra, combinatorics, or graph theory.
 

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Contents

INTRODUCTION 1
v
Discrete dynamical systems
11
Fixed graphs
18
Nonincreasing parameters and convergence
30
Invariants
36
Connected components
43
Subgraphdefined operators
57
Constructing infinite periodic graphs
65
Powerlike operators
97
Miscellaneous tools
104
Intersection graph operators
119
Other subgraphdefined operators
132
Powerlike operators
152
Shrinking or expanding operators
171
Composed operators
181
Digraph operators
195

Admissible graph posets
72
Roots
80
Decision problems
88

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