The Application Of Graph Theory In Chemistry Energy And Network

The research on graph energy is a very active research direction in the graph theory. If we supposed that G is a limited, simple, and undirected graph, that it has n nodes and m edges, that A(G) = (a_ij)_n×n is the adjacentmatrix of G andλ₁,λ₂,…,λ_n are named n characteristic values of A(G),namely,the characteristic values of graph G, E(G) =sum from i=1 to i=n|λ_i| is named the energy ofgraph G. In chemistry domain,the heat energy prodeuced by the generation of conjugated molecule is nearly equal toÏ€-the electronic total energy of the molecule, But the computation ofÏ€-the electronic total energy of themolecule may put the blame on computation of E(G) = sum from i=1 to i=n|λ_i|. Accordingto the main results of several kinds of graph energy, The ariticle discussed the energy of unicyclic.Unicyclic graph is a quite special kind of graph in graph theory.If a side is removed from its circle, it will turn to be a tree.Its energy computation is much simpler than any other graph algorithm.A pair of cospectral equienergetic graphs have been found in this dissertation Through studying the characteristic of unicyclic graph.In graph theory, Another active research direction is in the network routing algorithm.In the network's topological model,as the hyper cube Q_nhas good topological property,it can become the computer ultra massively parallel computer internet's structural model.In hypercube.In studying its fault-tolerant routing aspect,the safety vector is playing a very important role.In Wu Jie's article,every node's safety vector must undergo a n-1 turns computation,the computation is quite trouble some.Based on this,the article improve the safety vector definition,and determine the node's safety vetor through its safety matrix.The method's advantage is not only having a simple computation,but judging whether there is the most superior path between the node and any other node to which the distance from the node is k.This first chapter is the introduction part.The second chapter covers the energy concept as well as the computations and nature of several kinds of special graph energy.Through computation comparison,it invovles the computationmethod of partial graph energy and several pairs of equienergetic graph,and emphatically discussed the unicyclic graph energy.The third chapterhas analyzed the hypercube Structure feature.According to the safety vector's definition, the safety vector is improved,and the mothed of computingthe node's safety vector is drawn through its safety matrix. The fourth chapter is the summary.