The Laplacians, Kirchhoff index and complexity of linear Möbius and
cylinder octagonal-quadrilateral networks
Abstract
Spectrum graph theory not only facilitate comprehensively reflflect the
topological structure and dynamic characteristics of networks, but also
offer signifificant and noteworthy applications in theoretical
chemistry, network science and other fifields. Let Ln (8, 4) represent a
linear octagonal-quadrilateral network, consisting of n eight-member
ring and n four-member ring. The M¨obius graph Qn(8, 4) is constructed
by reverse identifying the opposite edges, whereas cylinder graph Q’n
(8, 4) identififies the opposite edges by order. In this paper, the
explicit formulas of Kirchhoffff indices and complexity of Qn(8, 4) and
Q‘n (8, 4) are demonstrated by Laplacian characteristic polynomials
according to decomposition theorem and Vieta’s theorem. In surprise, the
Kirchhoffff index of Qn(8, 4)(Q’n (8, 4)) is approximately one-third
half of its Wiener index as n → ∞.