| In recent years,graph theory has developed rapidly as a new subject,and has been widely used in operations research,biology,network theory,information theory,cybernetics,game theory,computer science and other fields.As early as the end of the 19th century,some scholars used graph theory to study the molecular structure of organic chemistry,where the vertices of simple undirected graphs can be regarded as compound atoms in the molecule,and each edge can be regarded as of the chemical bonds between atoms,so we can use the graphs of graph theory to represent the molecular structure of the compounds,and the research of graph theory is combined with chemical field.As one of the important branches of graph theory,Chemical graph theory is mainly used to study the topological invariants of molecular graphs in chemistry,also known as topological index.The topological index studied in this paper is the general sum-connectivity index,which is expressed as(?) in which a is any real number.With the rapid development of chemical graph theory,the study of topological index has been extended from the molecular graph to a series of graph operations,such as product graph,union of graph,etc.In this paper,we extend the sharp bounds on general sum-connectivity index of graphs for operations based on the cartesian product to the sharp bounds on general sum-connectivity index of graphs for operations based on the lexicographical product.Then according to the four operations based on the lexicographical product and the Cartesian product graph,the four operations based on the strong product are given,and the sharp bounds on general sum-connectivity index of graph for operations based on the strong product are calculated.Finally,for each theorem,an example of operation graph is given,the general sum-connectivity index are calculated,and the results are compared with the sharp bounds in the theorem,so as to verify the theorem. |
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