Block circulant graphs and the graphs of critical pairs of crowns

Rebecca E. Garcia, Pamela E. Harris, Bethany Kubik, Shannon Talbott

Abstract


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


Keywords


circulant matrix, order dimension, bipartite poset, chromatic number

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DOI: http://dx.doi.org/10.5614/ejgta.2019.7.2.1

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ISSN: 2338-2287

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