On The Nullity Of Tricycle Graphs

The graph G=(V,E)in this paper are simple undirected graphs with vertexset V={v₁,v₂,…,v_n},The adjacency matrix A(G)of graph G of order n isthe n×n symmetric matrix[a_ij],such that[a_ij=1]if[v_i]and[v_j]are adjacentand 0,otherwise.The characteristic polynomial of the graph G is P(G;λ)=det(λI_n-A).The roots of P(G;λ)are the eigenvalues of G,and to form the spectrum of the graphs.The number of zero eigenvalues in the spectrum of thegraph G is called its nullity,and is denoted byη(G).Let (?) is the set of allsimple undirected graphs.N={η(G)|G∈(?)},the set N is said to be the nullityset of (?).In this thesis we discuss the nullity and nullity set of simple undirectedtricycle graphs.