The (Multiplicative Degree-) Kirchhoff Index of Graphs Derived from the Cartesian Product of Sn and K2

Abstract

It is well known that many topological indices have widespread use in lots of fields about scientific research, and the Kirchhoff index plays a major role in many different sectors over the years. 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 Sn×K2, the Cartesian product of the star Sn, and the complete graph K2. In the present study, we completely solve this problem, that is, the explicit closed-form formulae of the Kirchhoff index, multiplicative degree-Kirchhoff index, and number of spanning trees are obtained for some graphs derived from Sn×K2.