Erich Prisner

Graph Dynamics

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 or 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 regarding 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 II addresses the operators themselves and lists all known graph operators grouped together in families, recounting, with complete references, all that is known about the dynamic behavior of these concrete operators.

The teaching and research experience of Erich Prisner includes the University of Louisville, the University of Maryland University College (Schwäbisch Gmünd), the Technical University of Cottbus (Germany), the Technical University of Berlin, and Franklin College.  Dr. Prisner has published extensively on intersection graphs and graph-theoretic operators.  A recipient of numerous research awards and grants, he also has been particularly active in integrating information technology in his teaching.

Graph Dynamics. CRC Press, 1995.