The Difference About The Wiener Index Of The Tree And Its Common Neighborhood Graph

The Wiener index of a connected graph is defined as the sum of distances between all unordered pairs of its vertices.If G is a simple graph,then con(G)the common neighborhood graph of G,has the same vertex set as G,and two vertices of con(G)are adjacent if they have a common neighbor in G.In this paper,the lower bound and the upper bound of the difference between the Wiener index of the tree and its common neighborhood graph are obtained respectively.The thesis mainly studies The Difference about the Wiener Index of the Tree and Its Common Neighborhood Graph,The specific structure is arranged as follows:In the first chapter,we introduce the definition and the background of the Wiener index of the tree and its common neighborhood graph,give the basic notations and terminology related to this thesis.In the second chapter,we reprove the theorem:the Wiener index of the tree less than or equal to the Wiener index of its common neighborhood graph.In the three chapter,we study the Wiener index of the tree and its common neigh-borhood graph,and the lower bound and the upper bound of the difference between the Wiener index of the tree and its common neighborhood graph are obtained respectively.