The Security Numbers Of Some Special Graphs

Let G=(V, E) be a graph. A subset S c V is secure if for each subset X c S,|N[X] n S|≥|N[X] n S|. The security number of G, denoted by s(G), is the smallest cardinality of a secure set in G.In this thesis, we first show the elementary properties, characterizations and the research results of secure sets. Using the method in solving the security number of two-dimensional grid-like graph, we establish security numbers of some special graphs:●s(K1,m□K1,n)=min{m+1, n+1};●s(Kq,m×K1,n)＝1:●s(K1,3□W1,3)=4;●s(W1,m□W1,n)≥min{2(m+1),2(n+1),12}, m>3, n>3.