2 research outputs found
Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs
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.Comment: In this paper, 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 grap
The Laplacian spectrum, Kirchhoff index and complexity of the linear heptagonal networks
Let be the linear heptagonal networks with heptagons. We study the
structure properties and the eigenvalues of the linear heptagonal networks.
According to the Laplacian polynomial of , we utilize the decomposition
theorem. Thus, the Laplacian spectrum of is created by eigenvalues of a
pair of matrices: and of order number and ,
respectively. On the basis of the roots and coefficients of their
characteristic polynomials of and , we not only get the explicit
forms of Kirchhoff index, but also corresponding total complexity of