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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 × 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 × K 2 .

journal of mathematics

The (Multiplicative Degree-) Kirchhoff Index of Graphs Derived from the Cartesian Product of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </math>

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

The (Multiplicative Degree-) Kirchhoff Index of Graphs Derived from the Cartesian Product of $S_{n}$ and $K_{2}$