图的广义和连通指数作为新提出的一类分子拓扑指数, 在QSPR/QSAR 中有很大的应用价值. 树图、单圈图和双圈图的极值问题已取得很多结果, 而三圈图相关问题的研究较为复杂. 限制 - 1 \leqslant \alpha  < 0, 对三圈图的广义和连通指数进行了研究. 通过对三圈图的分析, 构造了一种图的变换, 指出在三圈图中广义和连通指
数的极小值必由其中的七种类型图取得. 然后通过悬挂边的变换, 最终得到三圈图广义和连通指 数的极小值并刻画了唯一的极图.

 As a new class of molecular topological index, the general sum-connectivity index of graphs is of great value in QSPR/QSAR. The extremal problems of
trees, unicyclic graphs and bicyclic graphs has got many results, and the research in tricyclic graphs is more complicated. In this paper, by limiting  - 1 \leqslant \alpha  < 0, we study the general sum-connectivity index of tricyclic graphs. Based on the analysis of tricyclic graphs, one kind of graphic transformations is
constructed. It is pointed out that minimum general sum-connectivity index of tricyclic graphs must be obtained from the seven kinds of graphs. Then, by means of the transformation of the pendent edges, we obtain minimum general sum-connectivity index of tricyclic graphs and characterize the unique extremal graphs.