Let Π be a polar space of type Dn. Denote by Gδ(Π), δ ∈ {+,−} the associated half-spin Grassmannians and write Γδ(Π) for the corresponding half-spin Grassmann graphs. In the case when n ≥ 4 is even, the apartments of Gδ(Π) will be characterized as the images of isometric embeddings of the half-cube graph 1 2 Hn in Γδ(Π). As an application, we describe all isometric embeddings of Γδ(Π) in the ha...

We consider the Grassmann graph of k-dimensional subspaces an n-dimensional vector space over q-element field and its subgraph Γ(n,k)q which consists all non-degenerate linear [n,k]q codes. assume that 1<k<n−1. It is well-known every automorphism induced by a semilinear corresponding or isomorphism to dual second possibility realized only for n=2k. Our result following: if q≥3 k≠2, then can be ...

In this paper, we present the first application of Hoffman graphs for spectral characterizations of graphs. In particular, we show that the 2clique extension of the (t+ 1)× (t+ 1)-grid is determined by its spectrum when t is large enough. This result will help to show that the Grassmann graph J2(2D,D) is determined by its intersection numbers as a distance regular graph, if D is large enough.

We prove that pseudorandom sets in Grassmann graph have near-perfect expansion as hypothesized in [4]. This completes the proof of the 2-to-2 Games Conjecture (albeit with imperfect completeness) as proposed in [15, 3], along with a contribution from [2, 14]. The Grassmann graph Grglobal contains induced subgraphs Grlocal that are themselves isomorphic to Grassmann graphs of lower orders. A set...

We describe a rich family of binary variables statistical mechanics models on a given planar graph which are equivalent to Gaussian Grassmann Graphical models (free fermions) defined on the same graph. Calculation of the partition function (weighted counting) for such a model is easy (of polynomial complexity) as reducible to evaluation of a Pfaffian of a matrix of size equal to twice the numbe...

Uniform spanning trees are a statistical model obtained by taking the set of all spanning trees on a given graph (such as a portion of a cubic lattice in d dimensions), with equal probability for each distinct tree. Some properties of such trees can be obtained in terms of the Laplacian matrix on the graph, by using Grassmann integrals. We use this to obtain exact exponents that bound those for...

The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph Gq(n,k) (whose vertices are the k-subspaces of Fq, and are adjacent if they intersect in a (k− 1)-subspace) for k ≥ 2. We find an upper bound on its metric dimension, which is ...

Gait recognition is important in a wide range of monitoring and surveillance applications. Gait information has often been used as evidence when other biometrics is indiscernible in the surveillance footage. Building on recent advances of the subspace-based approaches, we consider the problem of gait recognition on the Grassmann manifold. We show that by embedding the manifold into reproducing ...