Geodesic
The Smith and critical groups of Paley graphs
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 4, pp. 1013-1022.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

There is a Paley graph for each prime power $q$ such that $q\equiv 1\pmod 4$. The vertex set is the field ${\mathbb{F}_q}$, and two vertices $x$ and $y$ are joined by an edge if and only if $x-y$ is a nonzero square of ${\mathbb{F}_q}$. We compute the Smith normal forms of the adjacency matrix and Laplacian matrix of a Paley graph.
Classification : 05C25, 05B20, 15A21, 05E30
Keywords: critical group, sandpile group, chip-firing game, strongly regular graph, Paley graph, Smith normal form, Jacobi sums, Laplacian matrix 
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     title = {The {Smith} and critical groups of {Paley} graphs},
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Chandler, David B.; Sin, Peter; Xiang, Qing. The Smith and critical groups of Paley graphs. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 4, pp. 1013-1022. http://geodesic.mathdoc.fr/item/JAC_2015__41_4_a7/