Second largest eigenvalueWe classify the connected graphs with precisely three distinct eigenvalues and second largest eigenvalue at most 1.doi:10.1016/j.jctb.2017.09.004Cheng, Xi-MingGreaves, Gary R.W.Koolen,
Van Dam E. R.Nonregular graphs with three eigenvalues.The Journal of Combinatorics. 1998E.R. Van Dam, Nonregular graphs with three eigenvalues, J. Combin. Theory Ser. B 73 (1998) 101-118.E. R. van Dam. Nonregular graphs with three eigenvalues, J. Combin. Theory Ser. B 73 (1998)...
摘要: In this paper, we investigate properties of graphs with three distinct α-eigenvalues of the matrix A α. In particular, we show for some α the connected graph G = K n − e, G = K1 ∨ ( n K n) and some...关键词:...
Milekic´, On bipartite graphs with small number of Laplacian eigenvalues greater than two and three, Linear Multilinear Algebra 47 (2000) 205-215.M. Pettrovic, I. Gutman, M.Lepovic and B. Milekic, On Bipartite graphs with small number of Laplacian eigenvalues greater than two or three,...
Benguria: Optimal bounds of ratios of eigenvalues of one—dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials, Commun. Math. Phys. 124 (1989), 403–415. MATH ADS MathSciNet Google Scholar M.S. Ashbaugh, R.D. Benguria: A sharp bound for the ratio ...
We provide a characterization of such graphs Γ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex, where d +1 is the number of different eigenvalues of Γ. This can be seen as another ...
3. Let A be the usual v × b (0, 1) adjacency matrix of . If r − μ is not a multiple μ−λ eigenvalue of A, then b ≥ v. 4. If r = 2λ − μ, then r −μ μ−λ = −2. Furthermore, let be a connected regular r −μ graph with an eigenvalue of ...
Graphs with few distinct D-eigenvalues determined by their D-spectra Linear Algebra and its Applications, Volume 628, 2021, pp. 42-55 Xiaoling Zhang Signed graphs with three eigenvalues: Biregularity and beyond Linear Algebra and its Applications, Volume 621, 2021, pp. 272-295 Peter Rowlinson,...
The family of minimal forbidden graphs for the set of graphs with all eigenvalues at least −2 is described. It is shown that each minimal forbidden graph has at most 10 vertices and the bound is the best possible.VijayaKumarandS.B....
Tricyclic graphs with exactly two main eigenvalues Gromov hyperbolicity of planar graphs On the minimal length of the longest trail in a fixed edge-density graph Real linear isometries between function algebras. II Thin sequences in the corona of H ∞ Einstein-Weyl structures on lightlike...