Exponent-critical primitive graphs and the Kronecker product
| Main Authors: | O'Mahony, Olga; National University of Ireland, Galway, Ireland, Quinlan, Rachel; National University of Ireland, Galway, Ireland |
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| Other Authors: | College of Science, National University of Ireland, Galway |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2019
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/623 https://www.ejgta.org/index.php/ejgta/article/view/623/pdf_115 |
Daftar Isi:
- 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.