Fractals on Graphs: Graph Fractaloids - Softcover

CHO, ILWOO

Softcover

ISBN 10: 3639194470 ISBN 13: 9783639194470

Publisher: VDM Verlag, 2009

Synopsis

Recently, graphs have been studied and applied in various math and science fileds. In this monograph, we consider graphs with fractal property. Starting with graphs (combinatorial objects), we construct the corresponding groupoids (algebraic objects). The fractal property of graphs and groupoids is detected by the automata labelings (automata-theoretic objects). The groupoids with fractal property will be called graph fractaloids. By defining suitable representations of groupoids, we establish von Neumann algebras (operator-algebraic objects). As elements of the von Neumann algebras, we define the labeling operators (operator-theoretic objects) of graph fractaloids. In Part 1, by computing the free moments (free-probabilistic data) of the operators, we verify how the graph fractaloids act in the von Neumann algebras. Also, based on such computations, we can classify the graph fractaloids, in Part 2. Our classification shows the richness of graph fractaloids which are not fractal groups, in general. In Part 3, we show that, for any finite graph, there always exists a finite fractal graph containing it as its part.

About this title

About the Author

Master Degrees (Math): Sungkyunkwan Univ. (Korea), Univ. of Iowa (U. S.), Ph. D Degree (Math): Univ. of Iowa (U. S.), Currenct Position (from 2005): Assistant Professor at St. Ambrose Univ., Dep. of Mathematics.

Edition details

• Publisher: VDM Verlag
• Publication date: 2009
• Language: English
• ISBN 10: 3639194470
• ISBN 13: 9783639194470
• Binding: Paperback
• Number of pages: 92