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In this paper, we provide a natural bijection between a special family ofblock circulant graphs and the graphs of critical pairs of the posets known asgeneralized crowns. In particular, every graph in this family of blockcirculant graphs we investigate has a generating block row that follows asymmetric growth pattern of the all ones matrix. The natural bijection providesan upper bound on the chromatic number for this infinite family of graphs.

Block Circulant Graphs and the Graphs of Critical Pairs of a Crown