Study Of Bounds Of SDD Index Of Graphs And The Chemical Trees With Minimum ISDD Index

The topological index of a graph is derived from the graph invariant,which can well represent the chemical bonds between chemical atoms.In this thesis,the graph invariant,inequalities,and transformations of the graphs are used to obtain the bounds of the symmetric division deg index of the graphs and the chemical trees with minimum inverse symmetric division deg index.The first chapter introduces the symmetric division deg index,inverse symmetric division deg index,related basic concepts and definitions,and introduces the research status at home and abroad.In the first section of the second chapter studies the symmetric division deg index of the graph by applying the invariant of the graph,such as maximum degree and minimum degree,and depicts the correlated polar chart;In the second section,utilize the function and the well-known inequality are used to obtain some relationship between the symmetric division deg index and the inverse symmetric division deg index.Chapter 3 first transforms the graph to obtain some related lemma of chemical trees with the minimum inverse symmetric division deg index,and finally characterizes the smallest chemical tree with the inverse symmetric division deg index.