The Reciprocal Complementary Wiener Number And Hyper-wiener Index Of Graphs

Topological index is defined as number descriptor on compound molecular (skeleton)graph. This thesis studies mainly the reciprocal complementary Wiener number of a class oftrees with perfect matchings and odd diameter and the hyper-Wiener index of k-memberedring spiro chains.Suppose that G = (V (G),E(G)) is a connected graph. Then the reciprocal complemen-tary Wiener number (RCW) of G is defined as (?), whered(u,v|G) is the distance between vertices u and v, and d is the diameter of G; the hyper-Wiener index is defined as (?), where d(u,v) is thedistance between u and v of G.This thesis consists of three chapters in all.In the first chapter, we introduce the background of our study, and give the basic defini-tions.In the second chapter, we firstly define a class of trees with perfect matchings and odddiameter. We further establish some properties of the reciprocal complementary Wienernumber, and determine the trees with the smallest, the second smallest and the third smallestreciprocal complementary Wiener numbers.In the third chapter, we compute the hyper-Wiener indices of arbitrary k-membered ringspiro chains and determine the extremal k-membered ring spiro chains.