Some orbits of a two-vertex stabilizer in a Grassmann graph

2024/07/07 by Seong, Ian · 2 citations
#05E18 #05E30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.06239

Abstract

Let \mathbbF_q denote a finite field with q elements. Let n,k denote integers with n>2k≥ 6. Let V denote a vector space over \mathbbF_q that has dimension n. The vertex set of the Grassmann graph J_q(n,k) consists of the k-dimensional subspaces of V. Two vertices of J_q(n,k) are adjacent whenever their intersection has dimension k-1. Let ∂ denote the path-length distance function of J_q(n,k). Pick vertices x,y of J_q(n,k) such that 1<∂(x,y)

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• The nucleus of the Grassmann graph J_q(N,D)
• Counting edges of different types in a local graph of a Grassmann graph

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