The Extremal Values Of Two Topological Indices Of Graphs

The chemical graph theory is a branch of graph theory,in which molecular structures are instead of graph models.As a result molecular graphs are forming.Molecular graphs,acting as the graphical representations of molecular topological properties,are hubs of graph theory and chemistry.The molecular topological index is one of the most active research fields in modern chemical graph theory,especially in the field of computational chemistry on topological quantitative structure-property relation(QSPR)and quantitative structure-activity relation(QSAR).In this paper,we mainly consider the extremal values of two topological indices(F-index,RDDxt index)with respect to some special atlases.By the graph transformations,we determine the most values of them and the corresponding extremal graphs.In the first chapter,we show some basic concepts of graph which may be used in the following、the corresponding notation、some important topological indices and their research status,at the same time the structure of this paper is presented.In the second chapter,we mainly focus on the extremal values of F-index about four special atlases(the simple connected graphs with a given clique number、vertex-connectivity、edge-connectivity and matching number,respectively).Based on the acquisitions of maximum and minimum Forgotten indices,the corresponding extremal graphs are described completely.In the third chapter,we investigate the maximum reformulated reciprocal product-degree distance of all unicyclic graphs with given order with the method of narrowing continuously the range of the atlases by graph transformation,then the extremal graph is also characterized completely.In chapter four,we briefly summarize the main work of this article and give some questions needed to further research.