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<p>We give explicit formulas for resistance distance matrices and Moore-Penrose inverses of incidence and Laplacian matrices of ladder, circular ladder, and Möbius ladder graphs. As a result, we compute the Kirchhoff index of these graphs and give new combinatorial formulas for the number of their spanning trees.</p>

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Explicit Formulas for Matrices Associated to Ladder, Circular Ladder, and Möbius Ladder Graphs

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Ali Azimi,
  • M. Farrokhi D. G.

摘要

We give explicit formulas for resistance distance matrices and Moore-Penrose inverses of incidence and Laplacian matrices of ladder, circular ladder, and Möbius ladder graphs. As a result, we compute the Kirchhoff index of these graphs and give new combinatorial formulas for the number of their spanning trees.