Study On The Difference Between Some Topological Indices Of Graphs

The topological index of a graph not only has a good application in reflecting the physical chemistry properties of a compound molecule,such as boiling point,melting point,toxicity,etc.,at the same time,it also provides a lot of help in understanding the properties of graphs.In this paper,we study the difference between some topological indices of a graph.Let F_X,Y（G）denote the difference between two topological indices X and Y of G.For some special topological indices X and Y,the following results are obtained:1 We explore the effect of a graph transformation（contracting the cut edge and adding a new pendent edge）on the F_W,ε（G）,where W and ε are the Wiener index and eccentricity of a graph G,respectively.2 We provide the first three extreme values of F_R,H（T）and F_ABC,H（T）of the binary trees T,where R,H and ABC are the Randi index,Harmonic index and ABC index of a binary tree T,respectively.3 We give the first six extreme values of F_R,H（T）and F_ABC,H（T）for the chemical trees T.The above conclusions are effective for further understanding the structural features and properties of graphs.