Geodesic
Adjacency preservers, symmetric matrices, and cores
Journal of Algebraic Combinatorics, Tome 35 (2012) no. 4, pp. 633-647.

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

Summary: It is shown that the graph $\Gamma _{ n }$ that has the set of all $n\times n$ symmetric matrices over a finite field as the vertex set, with two matrices being adjacent if and only if the rank of their difference equals one, is a core if $n\geq 3$. Eigenvalues of the graph $\Gamma _{ n }$ are calculated as well.
Keywords: keywords core, adjacency preserver, symmetric matrix, finite field, eigenvalue of a graph, coloring, quadratic form 
@article{JAC_2012__35_4_a1,
     author = {Orel, Marko},
     title = {Adjacency preservers, symmetric matrices, and cores},
     journal = {Journal of Algebraic Combinatorics},
     pages = {633--647},
     publisher = {mathdoc},
     volume = {35},
     number = {4},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__35_4_a1/}
}
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Orel, Marko. Adjacency preservers, symmetric matrices, and cores. Journal of Algebraic Combinatorics, Tome 35 (2012) no. 4, pp. 633-647. http://geodesic.mathdoc.fr/item/JAC_2012__35_4_a1/