Computing the resistance distance of a network is a fundamental and classical topic. In the aspects of considering the resistances between any two points of the lattice networks, there are many studies associated with the ladder networks and ladderlike networks. But the resistances between any two points for more complex structures than ladder networks or ladderlike networks are still unknown. In this paper, a rather complicated structure which is named linear octagonal network is considered. Treelike octagonal systems are cata-condensed systems of octagons, which represent a class of polycyclic conjugated hydrocarbons. A linear octagonal network is a cata-condensed octagonal system with no branchings. Moreover, the resistances between any two points of a linear octagonal network are first determined. One finds that the effective resistances between new inserted points and others points of a linear octagonal network can be given by the effective resistances between two initial points which are inherited from the linear polyomino network.

中文翻译：

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线性八边形网络的电阻距离的完整表征

计算网络的电阻距离是一个基本而经典的话题。在考虑晶格网络的任何两个点之间的电阻的方面，有许多与梯形网络和梯形网络相关的研究。但是，对于任何比梯形网络或类似梯形网络更复杂的结构，两点之间的阻力仍然未知。本文考虑了一个相当复杂的结构，称为线性八边形网络。树状八边形系统是八边形的催化缩合系统，代表一类多环共轭烃。线性八边形网络是没有分支的催化稠密八边形系统。此外，首先确定线性八边形网络的任意两点之间的电阻。