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<p>Let <i>G</i> be a graph of order <i>n</i> and let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k\in \{1,2,\ldots ,n-1\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>∈</mo> <mo stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>. The <i>k</i>-token graph of <i>G</i> is the graph, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(F_k(G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>F</mi> <mi>k</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, whose vertices are all the <i>k</i>-subsets of vertices of <i>G</i>, where two such <i>k</i>-sets are adjacent whenever their symmetric difference is an edge of <i>G</i>. In this paper, we determine the automorphism group of the <i>k</i>-token graph of the complete bipartite graph <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(K_{m,n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>.</p>

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On the automorphism group of token graphs of complete bipartite graphs

  • 期刊论文

  • 发表日期：

    2025年9月17日

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  • Ruy Fabila-Monroy,
  • Ana Trujillo-Negrete

摘要

Let G be a graph of order n and let \(k\in \{1,2,\ldots ,n-1\}\) k ∈ { 1 , 2 , … , n - 1 } . The k-token graph of G is the graph, \(F_k(G)\) F k ( G ) , whose vertices are all the k-subsets of vertices of G, where two such k-sets are adjacent whenever their symmetric difference is an edge of G. In this paper, we determine the automorphism group of the k-token graph of the complete bipartite graph \(K_{m,n}\) K m , n .