On Degree Distance Index Of Various Categories Graphs

Degree distance is a kind of parameter related to vertex degree and distance in the graph.It is a variant of Wiener index which reflects certain physical and chemical properties of macromolecular organic matter.Since it was first proposed by Dobrynin,Kochetova and Gutman in 1994,the problems on the degree distance of the graph,the degree distance of extreme graph,the vertex degree distance of the graph and extreme value problem has been widely concerned.In this paper,we study the structure of three classes of graphs:the Macromolecule Graph of Newkome Tree,Spiro Hexagonal Chain,the degree distance of Extended Double Star Graph(vertex)and the degree distance sorting problem.(1)Based on the structure of Newkome dendrimers,a kind of tree Newkome dendrimer map--The Graph of Newkome Dendrimers is defined.Basing to the Macromolecule Graph of Newkome Tree "recursive structure,a decomposition method of the graph is proposed,The recursion method is used to study the vertex degree distance of the graph,and the explicit expression of the vertex degree distance and the degree distance of the graph of Newkome Dendrimers.(2)For the two kinds of special structures of the two bits-Spiro Hexagonal Chain and the three bits-Spiro Hexagonal Chain,Through using the structure property of"helix" and "solvability",the vertex degree distance of the two bits and three bits-Spiro Hexagonal Chain is studied by recursive method,the explicit expression of any vertex degree distance of the graph and the degree distance of graph are obtained.(3)The vertex degree distance of the Extended Double Star Graph is studied,the ordering of vertex degree distance values of vertices in graphs is given.It is proved that the maximum point of degree distance is the star point with multiple suspension points and the vertex degree distance between the centers of stars has a concavity.