Abstract
AbstractLet represent a linear octagonal‐quadrilateral network, consisting of n eight‐member rings and n four‐member rings. Such a graph contains a unique pair of opposite edges. The Möbius graph Qn(8, 4) is constructed by reverse identifying these opposite edges, whereas the cylinder graph Qn′(8, 4) identifies the opposite edges in the natural manner. In this paper, the explicit formulas for the Kirchhoff index and complexity of Qn(8, 4) and Qn′(8, 4) are deduced from Laplacian characteristic polynomials using to decomposition theorem and Vieta's theorem. A consequence is the surprising fact that the Kirchhoff index of Qn(8, 4) (resp. Qn′(8, 4)) is approximately a third (resp. half) of its Wiener index as .
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