چكيده به لاتين
This thesis is a survey of the second smallest eigenvalue of the Laplacian of a graph G, best-known as the algebraic connectivity of G, denoted a(G)=λ_2 (G). And on the Laplacian spread of a graph G with n vertices is defined to be L(G)=D(G)-A(G), where λ_n (G) and λ_2 (G) are the largest and the Second smallest laplacian eigenvalues of G , respectively. Let λ_2 (G) denote its second smallest laplacian eigenvalue, It was conjectured that{λ_2 (G)+λ_2 (G ̅ )}≥1, where G ̅ is the Complement of G . Finally, in this thesis we prove that max{λ_2 (G),λ_2 (G ̅)≥2/5.
