Abstract:

 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.

Key words: general sum-connectivity index, tricyclic graph, graphic transformations