论文信息 - A characterization of Grassmann graphs

A characterization of Grassmann graphs

Let q be a prime power and suppose that e and n are integers satisfying 1 ⩽ e ⩽ n − 1. Then the Grassmann graph Γ(e, q, n) has as vertices the e-dimensional subspaces of a vector space of dimension n over the field Fq, where two vertices are adjacent iff they meet in a subspace of dimension e − 1. In this paper, a characterization of Γ(e, q, n) in terms of parameters is obtained provided that e ≠ 2, n − 2, 12n, 12(n ± 1) and (e ≠ 12(n±2) if q ϵ {2, 3}) and (e ≠ 12(n ± 3) if q = 3). As a consequence we can show that these Grassmann graphs are uniquely determined as distance-regular graphs by their intersection arrays.

Klaus Metsch | K. Metsch

[1] Hans Cuypers. The dual of Pasch's axiom , 1992, Eur. J. Comb..

[2] On a Theorem of Cooperstein , 1983, Eur. J. Comb..

[3] A. Neumaier,et al. Distance Regular Graphs , 1989 .

[4] Paola Biondi. On Finite Grassmann Spaces , 1988 .

[5] Alan P. Sprague. Characterization of projective graphs , 1978, J. Comb. Theory, Ser. B.

[6] Klaus Metsch,et al. Improvement of Bruck's completion theorem , 1991, Des. Codes Cryptogr..

[7] Ernest E. Shult. A Remark on Grassmann Spaces and Half-spin Geometries , 1994, Eur. J. Comb..

[8] Ernest Shult. Surveys in Combinatorics: CHARACTERIZATIONS OF THE LIE INCIDENCE GEOMETRIES , 1983 .

[9] G. Tallini,et al. On a Characterization of Grassmann Space Representing the h-Dimensional Subspaces in a Projective Space , 1983 .

[10] ArjehM. Cohen,et al. A characterization of some geometries of Lie type , 1983 .

[11] Giuseppe Tallini. Finite Geometries and Designs: On a characterization of the Grassmann manifold representing the lines in a projective space , 1981 .

[12] Alan P. Sprague,et al. Characterization of projective incidence structures , 1976 .

[13] Bruce N. Cooperstein. Some geometries associated with parabolic representations of groups of Lie type , 1976 .

[14] Domenico Olanda,et al. A Characteristic Property of the Grassmann Manifold Representing the Lines of a Projective Space , 1984, Eur. J. Comb..