Geodesic
The A-like matrices for a hypercube
The electronic journal of linear algebra, Tome 22 (2011), pp. 796-809.

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

Summary: Let D denote a positive integer and let Q Ddenote the graph of the D-dimensional hypercube. Let X denote the vertex set of Q Dand let A $\in $Mat $X(R)$ denote the adjacency matrix of Q D. A matrix B $\in $Mat $X(R)$ is called A-like whenever both (i) BA = AB; (ii) for all x, y $\in X$ that are not equal or adjacent, the (x, y)-entry of B is zero. Let L denote the subspace of Mat $X(R)$ consisting of the A-like elements. The subspace L is decomposed into the direct sum of its symmetric part and antisymmetric part. A basis for each part is given. The dimensions of the symmetric part and antisymmetric part are D + 1 and D2 , respectively.
Classification : 05E30, 05C50
Keywords: A-like matrices, distance-regular graphs, hypercubes 
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Miklavic, Stefko; Terwilliger, Paul. The A-like matrices for a hypercube. The electronic journal of linear algebra, Tome 22 (2011), pp. 796-809. http://geodesic.mathdoc.fr/item/ELA_2011__22__a24/