The Bounds Of ISDD Index Of A Graph And The Maximum Of ISDD Index Of Unicyclic And Bicyclic Graphs

Topological index of graph is a way to numeralize molecular structure and plays an important role in organic chemistry,especially in the study of quantitative structure-property and structure-activity relationships.In this paper,the upper and lower bounds of ISDD index of graph are studied by using inequality and invariant of graph.It is proved that there is a linear relationship between ISDD index and SDD index under certain conditions.The maximum value of ISDD index of unicyclic and bicyclic graph and the corresponding polar graph characterization problem are studied.The first chapter introduces the topological index of graph,the related concepts of graph theory,and summarizes the research status of graph ISDD index and SDD index.The second chapter,some tight upper and lower bounds of the ISDD index are obtained by reasonable reduction of the inequality,and the relationship between the index and other indices is studied.It is proved that the ISDD index and SDD index are linearly correlated under certain conditions.The third chapter,the first ISDD index,the second ISDD index,the third ISDD index and the fourth ISDD index are determined in the n-vertex unicyclic graphs and he first ISDD index,the second ISDD index,the third ISDD index and the fourth ISDD index are determined in the n-vertex bicyclic graphs the and corresponding polar graph structure is obtained.