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On vertex-stabilizers of bipartite dual polar graphs
Štefko Miklavič, 2010, izvirni znanstveni članek

Opis: Let ▫$X,Y$▫ denote vertices of a bipartite dual polar graph, and let ▫$G_X$▫ and ▫$G_Y$▫ denote the stabilizers of ▫$X$▫ and ▫$Y$▫ in the full automorphism group of this graph. In this paper, a description of the orbits of ▫$G_X \cap G_Y$▫ in the cases when the distance between ▫$X$▫ and ▫$Y$▫ is 1 or 2, is given.
Ključne besede: dual polar graphs, automorphism group, quadratic form, isotropic subspace
Objavljeno v RUP: 15.10.2013; Ogledov: 2856; Prenosov: 124
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Adjacency preservers, symmetric matrices, and cores
Marko Orel, 2012, izvirni znanstveni članek

Opis: 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 ▫$n \ge 3$▫. Eigenvalues of the graph ▫$\Gamma_n$▫ are calculated as well.
Ključne besede: adjacency preserver, symmetric matrix, finite field, eigenvalue of a graph, coloring, quadratic form
Objavljeno v RUP: 15.10.2013; Ogledov: 3132; Prenosov: 141
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