The (Multiplicative Degree-) Kirchhoff Index of Graphs Derived from the Cartesian Product of S n and K 2

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 $S_n\times K_2$ , the Cartesian product of the star $S_n$ , and the complete graph $K_2$ . 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 $S_n\times K_2$ .