Resistance distance-based graph invariants and spanning trees of graphs derived from the strong prism of a star

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.