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Self-Similar Graphs
For any graph on vertices and for any {\em symmetric} subgraph of
, we construct an infinite sequence of graphs based on the pair
. The First graph in the sequence is , then at each stage replacing
every vertex of the previous graph by a copy of and every edge of the
previous graph by a copy of the new graph is constructed. We call these
graphs {\em self-similar} graphs. We are interested in delineating those pairs
for which the chromatic numbers of the graphs in the sequence are
bounded. Here we have some partial results. When is a complete graph and
is a special matching we show that every graph in the resulting sequence is
an {\em expander} graph.Comment: 13 pages, 1 tabl
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