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

Abstract

Let L n be a linear hexagonal chain with n hexagons. Let Lˆ2 n be the graph obtained by the strong prism of a linear hexagonal chain with n hexagons, i.e. the strong product of L n and K 2. In this paper, explicit expressions for degree-Kirchhoff index and number of spanning trees of Lˆ2 n are determined, respectively. Furthermore, it is interesting to find that the degree-Kirchhoff index of Lˆ2 n is almost one eighth of its Gutman index.