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arXiv · 2007.10674

The (multiplicative degree-)Kirchhoff index of graphs derived from the Catersian product of $S_n$ and $K_2$

Jia-Bao Liu·Xin-Bei Peng·Jiao-Jiao Gu·Wenshui Lin
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Abstract

Recently, Li et al. [Appl. Math. Comput. 382 (2020) 125335] proposed the problem of determining the Kirchhoff index and multiplicative degree-Kirchhoff index of graphs derived from $S_n \times K_2$, the Catersian product of the star $S_n$ and the complete graph $K_2$. In the present paper, we completely solve this problem. That is, the explicit closed-form formulae of Kirchhoff index, multiplicative degree-Kirchhoff index, and number of spanning trees are obtained for some graphs derived from $S_n \times K_2$.

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Jia-Bao Liu, Xin-Bei Peng, Jiao-Jiao Gu, Wenshui Lin. 2020-07-21. The (multiplicative degree-)Kirchhoff index of graphs derived from the Catersian product of $S_n$ and $K_2$. https://arxiv.org/abs/2007.10674

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