The Smith and critical groups of Paley graphs
Journal of Algebraic Combinatorics（2014）
Abstract
There is a Paley graph for each prime power q such that q≡ 1 4 . The vertex set is the field 𝔽_q , and two vertices x and y are joined by an edge if and only if x-y is a nonzero square of 𝔽_q . We compute the Smith normal forms of the adjacency matrix and Laplacian matrix of a Paley graph.
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Key words
Critical group,Sandpile group,Chip-firing game,Strongly regular graph,Paley graph,Smith normal form,Jacobi sums,Laplacian matrix
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