Smith and Critical groups of Polar Graphs

Abstract

We compute the elementary divisors of the adjacency and Laplacian matrices of families of polar graphs. These graphs have as vertices the isotropic one-dimensional subspaces of finite vector spaces with respect to non-degenerate forms, with adjacency given by orthogonality.

References in corpus (2)

• The Smith group and the critical group of the Grassmann graph of lines in finite projective space and of its complement
• The critical groups of the Peisert graphs $P^{\ast }(q)$

Cited by in corpus (2)

• The Smith normal form of the walk matrix of the Dynkin graph $D_n$ for $n\equiv 0(\mathrm{mod}4)$
• A Note on the Critical Groups of Strongly Regular Graphs and Their Generalizations