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September 10, 2025Open Access

Full Automorphism Group of (m, 2)-Graph in Finite Classical Polar Spaces

Key Points

The study determines the full automorphism group of the (m, 2)-graph in finite classical polar spaces.
Vertices in the (m, 2)-graph represent m-dimensional subspaces, with edges defined by subspace dimension criteria.
Adjacent vertices denote that the sum of two m-dimensional subspaces results in an (m + 2)-dimensional subspace.
The findings enhance understanding of the automorphism group's role within the structure of polar spaces.

Abstract

Let Q be the finite classical polar space of rank ν≥1 over Fq, and Qm be the set of all m-dimensional subspaces of Q. In this paper, we introduce the (m, 2)-graph with Qm as its vertex set, and two vertices P, Q are adjacent if and only if P + Q is an (m + 2)-dimensional subspace of Q. The full automorphism group of (m, 2)-graph is determined.

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