Graph Dynamics

1. Auflage 1995
ISBN: 978-0-582-28696-2
Verlag: Chapman and Hall/CRC

Buch, Englisch, Band 338, 248 Seiten, Format (B × H): 216 mm x 279 mm, Gewicht: 408 g

Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series

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.

Autoren/Hrsg.

Prisner, Erich

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie

Inhaltsverzeichnis

IntroductionPart I: THEORY FOR GENERAL OPERATORSDiscrete Dynamical SystemsFixed GraphsIncreasing Parameters, Divergence, and DepthNon-Increasing Parameters and ConvergenceInvariantsConnected ComponentsSubgraph-Defined OperatorsConstructing Infinite Periodic GraphsAdmissible Graph PosetsRootsDecision ProblemsPowerlike OperatorsMiscellaneous ToolsPART II: CONCRETE OPERATORSIntersection Graph OperatorsOther Subgraph-Defined OperatorsPowerlike OperatorsShrinking or Expanding OperatorsComposed OperatorsDigraph Operators