جستجوی مقالات مرتبط با کلیدواژه « eigenvalues of graphs » در نشریات گروه « ریاضی »

Let G be a simple graph with vertices v_1,..., v_n. The adjacency matrix of G denoted by A(G) is an n×n matrix whose the entry (i,j) is 1 if v_i and v_j are adjacent and is zero otherwise. By the eigenvalues of G we mean the eigenvalues of A(G). Let λ_1 (G)≥λ_2 (G)≥⋯≥λ_n (G) be the eigenvalues of G. In this paper we obtain some results related to graphs with at most three non-negative eigenvalues. We obtain all non-connected graphs with this property. In addition, we find some families of connected graphs with this property. In particular we study two following families of graphs:1. Graphs such as G with exactly two positive eigenvalues and one zero eigenvalues. In other words graphs such as G with λ_1 (G)>0 , λ_2 (G)>0 , λ_3 (G)=0 and λ_4 (G)0 , λ_2 (G)>0 , λ_3 (G)>0 and λ_4 (G)

Let G be a graph with eigenvalues 1(G) n(G). In this paper we nd all simple graphs G such that G has at most twelve vertices and G has exactly two non-negative eigenvalues. In other words we nd all graphs G on n vertices such that n  12 and 1(G)  0, 2(G)  0 and 3(G) 0, 2(G) > 0 and 3(G)