Open AccessThe automorphism group and fixing number of orthogonality graph over a vector space
Author(s) -
Shikun Ou,
Yongqiang Tan
Publication year - 2021
Publication title -
journal of algebra and its applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.64
H-Index - 29
eISSN - 1793-6829
pISSN - 0219-4988
DOI - 10.1142/s0219498823500135
Subject(s) - mathematics , combinatorics , inner automorphism , automorphism , vector space , automorphism group , discrete mathematics , pure mathematics
Let [Formula: see text] be a field, and [Formula: see text] the [Formula: see text]-dimensional row vector space over [Formula: see text]. The orthogonality graph [Formula: see text] of [Formula: see text] is an undirected simple graph which has [Formula: see text] as its vertex set, and for distinct [Formula: see text], [Formula: see text] if and only if [Formula: see text], where [Formula: see text] is the transpose of [Formula: see text]. When [Formula: see text] is finite, it is shown that any automorphism of [Formula: see text] can be decomposed into the product of a row-orthogonal automorphism and either a permutation automorphism or a field automorphism; moreover, the fixing number and metric dimension of [Formula: see text] are considered.