Lattices and Norton algebras of Johnson, Grassmann and Hamming graphs

2012/04/09 by Maldonado, C., Penazzi, D.
#05E30 #06D99 #17D99 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.1947

Abstract

To each of the Johnson, Grassmann and Hamming graphs we associate a lattice and characterize the eigenspaces of the adjacency operator in terms of this lattice . We also show that each level of the lattice induces in a natural way a tight frame for each eigenspace. For the most important eigenspace we compute explicitly the constant associated to the tight frame. Using the lattice we also give a formula for the product of the Norton algebra attached to that eigenspace.

Related

• Norton algebras of the Hamming Graphs via linear characters
• Nonassociativity of the Norton Algebras of some distance regular graphs
• Tight Frames for Eigenspaces of the Laplacian on Dual Polar Graphs
• Eigenfunctions and minimum 1-perfect bitrades in the Hamming graph
• The smallest eigenvalues of Hamming graphs, Johnson graphs and other\n distance-regular graphs with classical parameters