Sum-Connectivity Index

Graph theory is one of important branches in applied mathematics, there are many important applications in many aspects. With the development of graph theory, it combines with many application disciplines and form many branches, chemical graph theory is the most widely part in the branches. But the molecular topological index is one of the most extensive research fields in chemical graph theory.The thesis mainly studies the sum-connectivity index which belongs to molecular topological index, the specific structure is arranged as follows:In the first chapter, we mainly introduce the definition and the background of the sum-connectivity index, introduce the current studies of sum-connectivity,and the basic notations which will be used in this paper.In the second chapter, we investigate the sum-connectivity index and chromatic number of the simple graph, by the effect of removal of a minimum degree vertex on the sum-connectivity index, By the induction we get a relation between the sum-connectivity index and chromatic number, and give the condition when the sum-connectivity index equals to the chromatic number.In the three chapter, we investigate some inequalities for the Sum-connectivity index of graph operations containing the join, composition, corona product, cartesian product and symmetric difference of graphs, get the lower and upper bounds of graph operations on the sum-connectivity index.