### Abstract

Let G be a finite connected graph on n vertices with Laplacian spectrum 0 = λ_{1} < λ_{2} ≤... ≤ λ_{n}: The Kirchhoff index of G is defined by the formula The aim of this paper is to find an explicit analytical formula for the Kirchhoff index of Mobius ladder graph Mn = C2n(1; n) and Prism graph Prn = C_{n} x P_{2}. The obtained formulas provide a simple asymptotical behavior of both invariants as n is going to the infinity.

Original language | English |
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Article number | 117 |

Pages (from-to) | 1654-1661 |

Number of pages | 8 |

Journal | Siberian Electronic Mathematical Reports |

Volume | 16 |

DOIs | |

Publication status | Published - 21 Nov 2019 |

### Keywords

- Chebyshev polynomial
- Circulant graph
- Kirchhoff index
- Laplacian matrix
- Wiener index

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## Cite this

Baigonakova, G. A., & Mednykh, A. D. (2019). Elementary formulas for kirchhoff index of mobius ladder and prism graphs.

*Siberian Electronic Mathematical Reports*,*16*, 1654-1661. [117]. https://doi.org/10.33048/SEMI.2019.16.117