This analysis reveals the automorphisms and key parameters of nonzero component union graphs in finite vector spaces, suggesting deeper insights into their structure.
In a recent paper, Das introduced an undirected simple graph Γ(V), called nonzero component union graph on a finite dimensional vector space V, and studied some properties of Γ(V). At the end of the paper, he posed to characterize the automorphisms of Γ(V). In this paper, we describe the automorphisms of Γ(V) by a result on zero-divisor graphs, and calculate several parameters (including fixing number, metric dimension and distinguishing number) related to automorphisms of Γ(V) when the base field of V is finite. Among others, we consider the fixing number, metric dimension and distinguishing number for an induced subgraph of Γ(V).
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Ou et al. (2025) studied this question.
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