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The Kirchhoff Index and Spanning Trees of Möbius / Cylinder Octagonal Chain
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  • Jia-bao Liu,
  • Ting Zhang,
  • Miaosheng Feng,
  • Wenshui Lin
Jia-bao Liu
Anhui Jianzhu University
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Ting Zhang
Anhui Jianzhu University
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Miaosheng Feng
Xiamen University
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Wenshui Lin
Xiamen University
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Abstract

The Kirchhoff index and degree-Kirchhoff index have attracted extensive attentions due to their wide applications in physics and chemistry. These indices have been computed for many interesting graphs, such as linear polyomino chain, linear / Möbius / cylinder hexagonal chain, and linear octagonal chain. In the present paper, we consider Möbius octagonal chain (Mn) and cylinder octagonal chain (M’n). Explicit closed-form formulae of the Kirchhoff index and the number of spanning trees are obtained for Mn and M’n.