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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Bethany Kubik
Department of Mathematics and Statistics, University of Minnesota Duluth
Electrical & Electronics Engineering

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Block circulant graphs and the graphs of critical pairs of crowns Rebecca E. Garcia; Pamela E. Harris; Bethany Kubik; Shannon Talbott
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2019.7.2.1

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.
Co-Authors Pamela E. Harris Rebecca E. Garcia Shannon Talbott