Exponent-critical primitive graphs and the Kronecker product

Olga O'Mahony, Rachel Quinlan


A directed graph is primitive of exponent t if it contains walks of length t between all pairs of vertices, and t is minimal with this property. Moreover, it is exponent-critical if the deletion of any arc results in an imprimitive graph or in a primitive graph with strictly greater exponent. We establish necessary and sufficient conditions for the Kronecker product of a pair of graphs to be exponent-critical of prescribed exponent, defining some refinements of the concept of exponent-criticality in the process.


primitive graph, exponent, graph Kronecker product

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DOI: http://dx.doi.org/10.5614/ejgta.2019.7.2.10


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ISSN: 2338-2287

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