On the first eigenvalue of bipartite graphs
WebIf is the complete bipartite graph with , then it is easy to know that all the eigenvalues of are with multiplicities , respectively. Thus, . Now suppose that . We will show that must be a complete bipartite graph. Let be the eigenvalue of with multiplicity . First, assume that , then the rank of is 2, and thus, is a complete bipartite graph ... 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.
On the first eigenvalue of bipartite graphs
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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 … Web4 de nov. de 2016 · No, it is not true. The bipartite graph with two vertices and one edge has eigenvalues 2 and 0. I forgot to mention, that there are at least 2 edges. Still false. Take the bipartite graph on four vertices that has the form of the letter "N". Its eigenvalues are 2, 0, and ± 0.5857....
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 Laplacian of G in terms of the domination number. Web1 de dez. de 2024 · On the First Eigenvalue of Bipartite Graphs. Article. Full-text available. Oct 2008; ... For the smallest eigenvalue λn(G) of a bipartite graph G of order n with no isolated vertices, for α∈ ...
Web14 de fev. de 2024 · Let . U denote the class of all connected bipartite unicyclic graphs with a unique perfect matching, and for each . m ≥ 3, let . U n be the subclass of . U with … WebExamples. 1. The complete graph Kn has an adjacency matrix equal to A = J ¡ I, where J is the all-1’s matrix and I is the identity. The rank of J is 1, i.e. there is one nonzero …
Web16 de fev. de 2016 · 1. Definition Let G = U ∪ V is bipartite graph, where U and V are disjoint sets of size p and q, respectively. The complete bipartite graph denoted by K p, …
Web1 de nov. de 2011 · Further results on the least eigenvalue of connected graphs @article{Petrovic2011FurtherRO, title={Further results on the least eigenvalue of connected graphs}, author={Miroslav Petrovic and Tatjana Aleksic and Slobodan K. Simic}, journal={Linear Algebra and its Applications}, year={2011}, volume={435}, pages={2303 … british heart foundation home clearanceWeb9 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 … cap and license lmhcWebOn the First Eigenvalue of Bipartite Graphs Amitava Bhattacharya School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road, Colaba, Mumbai 400005, … british heart foundation home storesWeb1 de fev. de 2024 · In recent paper [6], Hua and Wang studied eigenvalues and eigenfunctions of p-Laplacians with Dirichlet boundary condition on graphs and identified the Cheeger constants. In this paper, we study the eigenvalue estimates of p -Laplacian on graphs by combining the methods in Riemannian manifolds and graphs. We first set … cap and leoWebThe 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 … british heart foundation house clearance costWebIn 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 … cap and helmetWeb1 de abr. de 2024 · A signed graph G σ is an ordered pair (V (G), E (G)), where V (G) and E (G) are the set of vertices and edges of G, respectively, along with a map σ that signs … cap and mikey