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<p>Let <i>G</i> be a finite simple graph with vertex set <i>V</i>(<i>G</i>). The 2-<i>token graph</i> <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F_2(G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>F</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of <i>G</i> is a graph with vertices, and the 2-subsets of <i>V</i>(<i>G</i>) such that two 2-subsets are adjacent if and only if their symmetric difference is exactly an edge of <i>G</i>. In two previous papers, the automorphism groups of the 2-token graphs of the <i>n</i>-dimensional hypercube and Hamming graph were determined. As a generalization of this, in this paper, we determine the automorphism group of the 2-token graph of the Cartesian product of connected regular graphs containing no induced cycles of length 4.</p>

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Automorphism groups of a class of 2-token graphs

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Ju Zhang,
  • Young Soo Kwon,
  • Jin-Xin Zhou

摘要

Let G be a finite simple graph with vertex set V(G). The 2-token graph \(F_2(G)\) F 2 ( G ) of G is a graph with vertices, and the 2-subsets of V(G) such that two 2-subsets are adjacent if and only if their symmetric difference is exactly an edge of G. In two previous papers, the automorphism groups of the 2-token graphs of the n-dimensional hypercube and Hamming graph were determined. As a generalization of this, in this paper, we determine the automorphism group of the 2-token graph of the Cartesian product of connected regular graphs containing no induced cycles of length 4.