  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 $S_n \times K_2$.
