论文标题
苯基链的最小基尔chhoff指数
The minimum Kirchhoff index of phenylene chains
论文作者
论文摘要
令$ g $为连接的图。 $ g $的任意两个顶点之间的电阻距离等于通过用单位电阻代替每个边缘来构建的相应电网中它们之间的有效电阻。 Kirchhoff指数定义为所有对顶点之间的电阻距离之和。最近，杨和王确定了苯链链的最大基尔chhoff指数，他们提出了关于最小基尔chhoff指数的猜想。在本说明中，我们表征了相对于Kirchhoff指数的最小苯链链。这证明了猜想。
Let $G$ be a connected graph. The resistance distance between any two vertices of $G$ is equal to the effective resistance between them in the corresponding electrical network constructed from $G$ by replacing each edge with a unit resistor. The Kirchhoff index is defined as the sum of resistance distances between all pairs of the vertices. Recently, Yang and Wang determined the maximum Kirchhoff index of phenylene chains, and they proposed a conjecture about the minimum Kirchhoff index. In this note, we characterized the minimum phenylene chains with respect to the Kirchhoff index. This proves the conjecture.
