Study Of Strictly Deza Graphs With Some Special Parameters

In 1963,the concept of strong regular graphs was first introduced by Bose:A k-regular graph ? with n vertices,if the concept ? and ? exist such that the number of common neighboring points of any two adjacent vertices in the graph ? is A,the common neighboring points of any two non-adjacent points in the graph is ?,the graph ? is called a strong regular graph.In 1999,the concept of strong regular graphs was generalized by Erickson M et al:A non-empty k-regular graph ? on n vertices is called a Dzea graph if there exist constants b and a(b? a)such that any pair of distinct vertices of ?has precisely either b or a common neighbours.The quantities n,k,b,and a are called the parameters of ? and are written as the quadruple(n,k,b,a).If a Deza graph has diameter 2 and is not strongly regular,then it is called a strictly Deza graph.In this paper,we investigate the existence of strictly Deza graph with some special parameters and the properties of strictly Deza graph with parameters(n,k,k-2,a).The research contents and structure of the article are listed as follows:The introduction briefly introduces the research background and current status of strictly Deza graph.In Chapter 1,we introduces some preparatory knowledge,the conditions to be met to construct a strictly Deza graph,and some conclusions need to be used in the proof process.In Chapter 2,we focus on the existence of strictly Deza graphs with parameters(n,k,k-1,k-3).In Chapter 3,we investigate the existence of strictly Deza graphs with parameters(n,k,k-3,k-5).In Chapter 4,we explore the existence of the strictly Deza graphs with(n,k,k-2,a)parameters when a takes different values.In Chapter 5,we study the properties of strictly Deza graphs with parameters(n,k,k-2,a).