The Extremal Value Of Some Topological Indices Over Class Of Tree

In this paper,we mainly study the extremal value of topological indices over Caterpillar tree,the properties which attain the extremal values,and the structures of extremal Caterpillars.These topological indices include Randic index,First Zagreb index,Albertson index,Forgotten topological index and the variation of the Randic index.Firstly,it is vertex-degree-based topological indices to Randic index,First Zagreb index,Albertson index,Forgotten topological index.For the extremal values of these indices,we characterize the general Caterpillar tree,and adjust the pendant vertices of two vertices,comparing the values of indices,and getting the extremal values and structures.Secondly,for the variation of the Randic index,we can't directly find the extremal value by the above method,but for given degree sequence ?=(d1,d2,…,dn)among all Caterpillar tree,where d1?d2?…?dk?dk+1=…?dn= 1,we can characterize the extremal Caterpillar tree which respec-tively attain the maximum and minimum variation of the Randic index,and adjust the degree of vertices to attained the extremal value and extremal tree of Caterpillars.Finally,we summarize these results.