Fractals on Graphs (Paperback)

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.

General

Imprint:	VDM Verlag
Country of origin:	Germany
Release date:	September 2009
First published:	September 2009
Authors:	Ilwoo Cho
Dimensions:	229 x 152 x 6mm (L x W x T)
Format:	Paperback - Trade
Pages:	92
ISBN-13:	978-3-639-19447-0
Categories:	Books > Science & Mathematics > Mathematics > General
LSN:	3-639-19447-0
Barcode:	9783639194470

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