Randić ordering of chemical trees Original Research Article

We study the behavior of the Randić index image subject to the operation on a tree T which creates a new tree image by deleting an edge ax of T and adding a new edge incident to either a or x. Let image be the smallest poset containing all pairs image such that image and image (where image is the collection of trees with n vertices and of maximum degree 4). We will determine the maximal and minimal elements of image. We present an algorithm to construct image-monotone chains of trees image such that image. As a corollary of our results, we present a new method to calculate the first values of image on image.