The variable connectivity index, introduced by the chemist Milan Randić in the first quarter of 1990s, for a graph is defined as , where is a non-negative real number and is the degree of a vertex in . We call this index as the variable Randić index and denote it by . In this paper, we show that the graph created from the star graph of order by adding an edge has the minimum value among all unicyclic graphs of a fixed order , for every and .

中文翻译：

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给定阶的单圈图的最小可变连通性指数

可变连接性指数，由化学家米兰·兰迪奇在20世纪90年代第一季度引入，一个图形被定义为，其中是一个非负实数并且为一个顶点的程度中。我们将此索引称为变量Randić索引，并用表示。在本文中，我们证明了在固定阶的所有单环图中，通过添加边缘从阶的星形图创建的图具有最小值，对于每个 和 。