Topological Indices Of Interconnection Networks And Its Applications

Graph theory mainly studies the internal structure of graphs.Chemical graph theory is an important research field combining mathematics and chemistry.It main-ly reflects the chemical and physical properties of substances with a specific molecular structure by means of the topological index of graphs,and studies the internal re-lations of their structures between the topological index of vertex degree and edge degree of graphs.In this thesis,we mainly studies the intrinsic relationship between the topolog-ical properties and network structure of several important networks which based on the degree of vertices and edges through the topological index of internal staggered networks(that is F-index,EM1(G)-index,K-edge index).The concrete content in-clude:· In Chapter 1,we mainly introduces the research background,research signifi-cance and research status of this paper.· In Chapter 2,we give some necessary definition,graph structure and lemmas.· In Chapter 3,we first precise define the number of vertices and edges of butterfly network by the dimension of butterfly network,and define the specific meaning of the pairs of vertices corresponding to the set of vertices of butterfly network,as well as the conditions for the adjacency of two different vertices.Then we are based on this condition and the characteristics of butterfly network,the normal and diamond expressions of three-dimensional butterfly network are drawn.Furthermore,the general formulas for calculating the F-index,EM1(G)-index,K-edge index of butterfly network are given.which are deduced according to the degree of vertices and edge.Finally,the three topological index are modeled and compared.· In Chapter 4.we first precise define the number of vertices and edges of Bene network by the dimension of Bene network.Then we are based on the char-acteristics of Bene network,the normal and diamond expressions of three-dimensional Bene network are drawn.Furthermore,the general formulas for calculating the F-index,EM1(G)-index,K-edge index of Bene network are giv-en which are deduced according to the degree of vertices and edges.Finally,the three topological index are modeled and compared.· In Chapter 5,we obtain two architectures by applying intermediate operations on m x'n grid and deleting vertices placed on the non-interface which based on dual graph of a planar graph,,that is,MDN1(m,n)network of the first grid-derived network and MDN2(m,n)network of the second grid-derived network.Firstly,we precisely define the number of vertices and edges in the whole net-work by using the vertices in rows and columns of the two grid-derived networks.Then the MDN1(5,5)network and MDN2(5,5)network are drawn respective-ly,according to the characteristics of these two kinds of grid-derived networks.Furthermore,the general formulas for calculating the F-index,EM1(G)-index,K-edge index of these two kinds of grid-derived networks are given which are deduced according to the degree of vertices and edges.Finally,we model and compare these three topological index.· In Chapter 6,we summarize the main results in this paper and give some prospects for further research in the future.