On the first eigenvalue of bipartite graphs
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 … Web30 de mar. de 2024 · The bipartite Kneser graph H(n, k) is the graph with the set of all k and n − k subsets of the set [n] = {1, 2, ..., n} as vertices, in which two vertices are adjacent if and only if one of them ...
On the first eigenvalue of bipartite graphs
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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∈ ... Webmatrices. In §3 we show that the maximum eigenvalue of a bipartite graph increases if we replace it by the corresponding chain graph. §4 gives upper estimates on the maximum …
Web18 de jan. de 2024 · Eigenvalues of signed graphs. Signed graphs have their edges labeled either as positive or negative. denote the -spectral radius of , where is a real symmetric graph matrix of . Obviously, . Let be the adjacency matrix of and be a signed complete graph whose negative edges induce a subgraph . In this paper, we first focus … Web1 de jan. de 2009 · In particular, using Perron-Frobenius theory, we establish a characterization for bipartite graphs in terms of the set of eigenvalues of gain graph and the set of eigenvalues of the underlying graph.
WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this paper we study the maximum value of the largest eigenvalue for simple bipartite graphs, … 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 …
Web21 de abr. de 2024 · For (a) you first prove that k is an eigenvalue of G 's adjacency matrix A. This is simple and is already explained in Hidalgo's answer: A − k I is not invertible. …
Web15 de jan. de 2010 · On the first eigenvalue of bipartite graphs. Electron. J. Combin., 15 (2008), p. #R144. Google Scholar [2] Xiang En Chen. On the largest eigenvalues of trees. Discrete Math., 285 (2004), pp. 47-55. View PDF View article Google Scholar [3] M. Hofmeister. On the two largest eigenvalues of trees. how big are wolf spidersWeb1 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 … how many movies has lin shaye been inWebidentifying the bipartite structure of signed networks using data-driven methods [31], furthering work done by Facchetti et al. [32], and Harary and Kabell [33]. The contributions of this paper are twofold. First, we show that the property of structural balance, when com-bined with symmetries in the underlying graph, as well how many movies has robert de niro been inWeb82 Expander Graphs chains). In addition, for most settings of parameters, it is impossible to have expansion larger than D −1 (as shown in Problem 4.3). We prove a slightly simpler theorem for bipartite expanders. Definition 4.3. A bipartite multigraph G isa(K,A) vertex expander if for all sets S of left-vertices of size at most K, the ... how many movies has steven spielberg directedWebThis paper studies the consensus of first-order discrete-time multi-agent systems with fixed and switching topology, and there exists cooperative and antagonistic interactions among agents. A signed graph is used to model the interactions among agents, and some sufficient conditions for consensus are obtained by analyzing the eigenvalues of a Laplacian … how many movies has luis guzman been inWeb11 de set. de 2024 · We have studied the local unitary equivalence of quantum states in terms of invariants. In bipartite system, we expand quantum states in Bloch representation first. Then some invariants under local unitary transformation are constructed by the products of coefficient matrices, the singular values of coefficient matrix and the … how many movies has shiloh nelson been inWeb19 de fev. de 2024 · The fact that $\lambda = \sqrt{cd}$ is the largest eigenvalue of our adjacency matrix follows from the Perron-Frobenius theorem, which states that an … how many movies has keanu reeves done