Block circulant graphs and the graphs of critical pairs of crowns - Rebecca E. Garcia; Pamela E. Harris; Bethany Kubik; Shannon Talbott (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2019)
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.