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<p>Counting spanning trees in graphs and networks is an attractive topic to mathematicians and statistical physicists. Very recently, Li and Yan considered the problem of counting spanning trees with one perfect matching in linear hexagonal chains. Lai and Zhu further considered linear <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((4k+2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-chains. We extend these results to helicene <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((4k+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-polygonal chains which commonly appear in molecular and crystal structures.</p>

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Counting Spanning Trees with One Perfect Matching in Helicene Polygonal Chains on the Plane and Cylinder

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Sujing Cheng,
  • Jun Ge

摘要

Counting spanning trees in graphs and networks is an attractive topic to mathematicians and statistical physicists. Very recently, Li and Yan considered the problem of counting spanning trees with one perfect matching in linear hexagonal chains. Lai and Zhu further considered linear \((4k+2)\) ( 4 k + 2 ) -chains. We extend these results to helicene \((4k+1)\) ( 4 k + 1 ) -polygonal chains which commonly appear in molecular and crystal structures.