Randi? ordering of chemical trees
We study the behavior of the Randi? index ? ? subject to the operation on a tree T  which creates a new tree T??T T ? ? T by deleting an edge ax of T and adding a new edge incident to either a or x . Let ?mso ? mso be the smallest poset containing all pairs (T,T?) ( T , T ? ) such that ?(T)<?(T?) ? ( T ) < ? ( T ? ) and T,T??Cn T , T ? ? C n (where Cn C n is the collection of trees with n  vertices and of maximum degree 4). We will determine the maximal and minimal elements of (Cn,?mso) ( C n , ? mso ) . We present an algorithm to construct ? ? -monotone chains of trees T0,T1,T2,,Tm T 0 , T 1 , T 2 ,  , T m such that Ti?msoTi+1 T i ? mso T i + 1 . As a corollary of our results, we present a new method to calculate the first values of ? ? on Cn C n .
chemical trees randi? index connectivity index partial ordering