Abstract Let S n 2 be the graph obtained by the strong prism of a star Sn, i.e. the strong product of K2 and Sn. In this paper, explicit expressions for Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning tress of S n 2 are determined, respectively. More specially, let S n , r 2 be the set of subgraphs obtained by randomly deleting r vertical edges from S n 2 , where 0 ≤ r ≤ n. Explicit formulas for Kirchhoff index and number of spanning trees for any graph S n , r 2 ∈ S n , r 2 are established, respectively. Moreover, the Kirchhoff index of S n , r 2 is almost three-eighths of its Wiener index.

中文翻译：

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基于电阻距离的图不变量和从恒星的强棱镜导出的图的生成树

摘要 设Sn 2 为恒星Sn 的强棱镜得到的图，即K2 和Sn 的强积。本文分别确定了基尔霍夫指数、乘性度-基尔霍夫指数和S n 2 的跨度数的显式表达式。更具体地说，令 S n , r 2 为从 S n 2 中随机删除 r 条垂直边获得的子图集合，其中 0 ≤ r ≤ n。分别建立了任意图 S n , r 2 ∈ S n , r 2 的 Kirchhoff 指数和生成树数的显式公式。此外，S n ，r 2 的基尔霍夫指数几乎是其维纳指数的八分之三。