三圈图的极小广义和连通指数  

Minimum general sum-connectivity index of tricyclic graphs

作　　者：秦倩楠 邵燕灵[1] 

机构地区：[1]中北大学理学院,太原030051

出　　处：《运筹学学报》2018年第1期142-150,共9页Operations Research Transactions

基　　金：国家自然科学基金(No.11071227)

摘　　要：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≤α<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.

关 键 词：广义和连通指数 三圈图 图的变换 

分 类 号：O157.5[理学—数学]