On The Hosoya Index Of Wei Ghted Chemical Trees

The Hosoya index is defined as the total number of matchings of a simple graph.We generalize the index to the weighted chemical tree W in this thesis.The index is redefined as the sum of the Hosoya index of each weight.ed forest which is induced by all edges with the same weight in W.The main work is as following:In the first chapter,we first introduce the research background of graph theory and Hosoya index,then briefly explain the research progress and main results related to this index,and finally introduce the symbols,basic concepts and main lemmas,which will be applied in this thesis.In the next chapter,we develop a algorithm for calculating the index of weighted chemical trees with the complexity of O(nlog2n),and characterize extremal trees among all weighted chemical trees of given order based on the background of chemistry.In the last chapter,the upper and lower bounds of the Hosoya indices corresponding to the extremal graphs do not reflect the richer information.We first establish models of random tree and random weighted tree,and then present the global distribution of tree and weighted tree about the index under these two models.More precisely,according to data fitting of index by using Mathematica,we conclude that the index follows a normal distribution with respect to the models.