Graph Dynamics
Seiten
1995
Longman (Verlag)
978-0-582-28696-2 (ISBN)
Longman (Verlag)
978-0-582-28696-2 (ISBN)
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This text is concerned with the iterated behaviour of graphs under certain graph-valued functions. Although the relevance of many of the concrete operators may be questionable, there are several unifying principles in the investigation of such discrete dynamical systems.
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.
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.
Introduction
Part I: THEORY FOR GENERAL OPERATORS
Discrete Dynamical Systems
Fixed Graphs
Increasing Parameters, Divergence, and Depth
Non-Increasing Parameters and Convergence
Invariants
Connected Components
Subgraph-Defined Operators
Constructing Infinite Periodic Graphs
Admissible Graph Posets
Roots
Decision Problems
Powerlike Operators
Miscellaneous Tools
PART II: CONCRETE OPERATORS
Intersection Graph Operators
Other Subgraph-Defined Operators
Powerlike Operators
Shrinking or Expanding Operators
Composed Operators
Digraph Operators
| Erscheint lt. Verlag | 22.11.1995 |
|---|---|
| Reihe/Serie | Chapman & Hall/CRC Research Notes in Mathematics Series ; 338 |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 216 x 279 mm |
| Gewicht | 408 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| ISBN-10 | 0-582-28696-4 / 0582286964 |
| ISBN-13 | 978-0-582-28696-2 / 9780582286962 |
| Zustand | Neuware |
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