Web3 de mai. de 2016 · 1-If λ is eigenvalue of G ′ with multiplicity l then − λ is also eigenvalue of G ′ with multiplicity l (since G ′ is bipartite graph, see Lemma 3.13 and Theorem 3.14 in this book ). 2-From here we know that if l vertices have the same neighbourhood (that is N ( u 1) = N ( u 2) =... = N ( u l) ), then 0 is eigenvalue with multiplicity ... Web21 de mar. de 2013 · Bhattacharya A, Friedland S, Peled UN: On the first eigenvalue of bipartite graphs. Electron. J. Comb. 2008., 15: Article ID #R144. Google Scholar Das KC: On conjectures involving second largest signless Laplacian eigenvalue of graphs. Linear Algebra Appl. 2010, 432: 3018–3029. 10.1016/j.laa.2010.01.005
(PDF) On the First Eigenvalue of Bipartite Graphs (2008)
Web27 de fev. de 2024 · We consider the set of real zero diagonal symmetric matrices whose underlying graph, if not told otherwise, is bipartite. Then we establish relations between the eigenvalues of such matrices and those arising from their bipartite complement. Some accounts on interval matrices are provided. We also provide a partial answer to the still … WebThe least ϵ -eigenvalue of unicyclic graphs. Let ξ i 1 > ξ i 2 > ⋯ > ξ i k be all the distinct ϵ -eigenvalues of a connected graph G. Then the ϵ -spectrum of G can be written as S p e c ϵ ( G) = ξ i 1 ξ i 2 … ξ i k m 1 m 2 … m k, where m j is the multiplicity of the eigenvalue ξ … cssmi outlook
The Adjacency Matrix and The nth Eigenvalue - Yale University
Web9 de abr. de 2024 · On the choosability of. -minor-free graphs. Given a graph , let us denote by and , respectively, the maximum chromatic number and the maximum list … WebIn this paper we study the maximum value of the largest eigenvalue for simple bipartite graphs, where the number of edges is given and the number of vertices on each side of the bipartition is given. We state a conjectured solution, which is an analog of the Brualdi-Hoffman conjecture for general graphs, and prove the conjecture in some special cases. WebLet G be a connected non-bipartite graph on n vertices with domination number @c@?n+13. We present a lower bound for the least eigenvalue of the signless … css misscount