On the critical group of the missing Moore graph

```@article{Ducey2017OnTC,
title={On the critical group of the missing Moore graph},
author={Joshua E. Ducey},
journal={Discret. Math.},
year={2017},
volume={340},
pages={1104-1109}
}```
• Joshua E. Ducey
• Published 1 September 2015
• Mathematics, Computer Science
• Discret. Math.
We consider the critical group of a hypothetical Moore graph of diameter \$2\$ and valency \$57\$. Determining this group is equivalent to finding the Smith normal form of the Laplacian matrix of such a graph. We show that all of the Sylow \$p\$-subgroups of the critical group must be elementary abelian with the exception of \$p = 5\$. We prove that the \$5\$-rank of the Laplacian matrix determines the critical group up to two possibilities.
7 Citations

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