Expander Constructions ( Zig - Zag Expanders ) Lecturer : Cynthia
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چکیده
Construction 7.1 (Margulis [Mar]) Fix a positive integerM and let [M ] = {1, 2, . . . ,M}. Define the bipartite graph G = (V,E) as follows. Let V = [M ]2∪ [M ]2, where vertices in the first partite set are denoted (x, y)1 and vertices in the second partite set are denoted (x, y)2. From each vertex (x, y)1, put in edges to (x, y)2, (x, x+ y)2, (x, x+ y+1)2, (x+ y, y)2, and (x+ y+ 1, y)2, where all arithmetic is done modulo M . Then G is an expander. The proof uses Fourier analysis.
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