n维立方体电路的电阻分析

On the Resistance of n Cube Circuit

在一个ｎ维立方体的每一条边上串一个１Ω的电阻之后就得到了一个特殊的电路．计算此电路中任意两点之间的电阻值是一个有意义但难度较大的问题．国外学者Ｎａｒａｗａｙ分别于１９９３年和１９９４年求出了当两点之间的距离为１，２和ｎ时的电阻值．我们则首次求出了当两点之间的距离为ｎ－１时的电阻值．还具体算出了ｎ≤７的所有电阻值。

It is very interesting and difficult to calculate the resistance seen into the port of a n cube, with each edge a resistor of 1Ω, formed by two given vertices. Dr. Narraway found the values of such resistance, when the distance of the two vertices are 1,2 or n, in 1993 and 1994 respectively. This paper initially finds another value of the resistance when the two vertices are n-1 apart from each other. All possible resistances are found for the cases of 1≤n≤7 too. Open problems are presnted in the conclusions.