  Resistance distance is a novel distance function, also a new intrinsic graph
metric, which makes some extensions of ordinary distance. Let On be a linear
crossed octagonal graph. Recently, Pan and Li (2018) derived the closed
formulas for the Kirchhoff index, multiplicative degree-Kirchhoff index and the
number of spanning trees of Hn. They pointed that it is interesting to give the
explicit formulas for the Kirchhoff and multiplicative degree-Kirchhoff indices
of On. Inspired by these, in this paper, two resistance distance-based graph
invariants, namely, Kirchhoff and multiplicative degree-Kirchhoff indices are
studied. We firstly determine formulas for the Laplacian (normalized Laplacian,
resp.) spectrum of On. Further, the formulas for those two resistance
distance-based graph invariants and spanning trees are given. More surprising,
we find that the Kirchhoff (multiplicative degree-Kirchhoff, resp.) index is
almost one quarter to Wiener (Gutman, resp.) index of a linear crossed
octagonal graph.
