Minimum general Randic index on chemical trees with given order and number of pendent vertices
The general Randic index R-alpha(G) of a (chemical) graph G, which is also called the connectivity index, is defined as the sum of the weights (d(u)d(v))(alpha) of all edges uv of G, where d(u) denotes the degree of a vertex u in C and a is an arbitrary real number. In this paper, we consider chemical trees (with maximum degree at most 4) with a given order and number of pendent vertices and determine the extremal trees with the minimum general Randic index for arbitrary or among this class of trees. For alpha > 1 we also give a sharp lower bound of the general Randic index for general trees (without degree restriction) with a given order and number of pendent vertices.
chemical tree pendent vertex linear programming