Research On Some Problems Of Graph Theory

The main objective of studying on the determinant of the adjacency matrix of a graph is to study the multiplicity of zero eigenvalue,which is widely applied in the stability problem of the chemical molecular structure graph.The determinants of the adjacency matrices of a graph with one cycle and a graph with bicycle are given in the second chapter of this thesis.For given n,s₁,s₂,the relationship between the four parameters of the L-shape tile L(n;l,h,p,q)of Double Loop Graph DLG(n;s₁,s₂)and the L-shape tile L(2n;l′,h′,p′,q′)of Bi-Cayley Graph BC(n;s₁,s₂)is given in the third chapter of this thesis.