The normalized Laplacian, degree-Kirchhoff index and spanning trees of graphs derived from the strong prism of linear polyomino chain

Abstract

Let $B_n$ be a linear polyomino chain with $n$ squares. Let $B_n^2$ be the graph obtained by the strong prism of a linear polyomino chain with $n$ squares, i.e. the strong product of $K_2$ and $B_n$. In this paper, explicit expressions for degree-Kirchhoff index and number of spanning trees of $B^2_n$ are determined, respectively. Furthermore, it is interesting to find that the degree-Kirchhoff index of $B^2_n$ is almost one eighth of its Gutman index.