Results 41 to 50 of about 169,163 (265)
Linear Algebra and its Applications, 2009 It is shown that only a fraction of \(2^{-\Omega(n)}\) of the graphs on \(n\) vertices have an integral spectrum. Although there are several explicit constructions of such graphs, no upper bound for their number has been known. Graphs of this type play an important role in quantum networks supporting the so-called perfect state transfer.
Ahmadi, Omran +3 more
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The spectral determination of the connected multicone graphs
AKCE International Journal of Graphs and Combinatorics, 2021 The main goal of the paper is to answer an unsolved problem. A multicone graph is defined to be the join of a clique and a regular graph, and a wheel as the join of a vertex and a cycle.
Ali Zeydi Abdian +4 more
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Frontiers in NeuroscienceIntroductionSubstance use disorders (SUDs) are heterogeneous diseases with overlapping biological mechanisms and often present with co-occurring disease, such as cardiovascular disease (CVD).
Everest Castaneda +3 more
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Eigenvalue −1 of the Vertex Quadrangulation of a 4-Regular Graph
AxiomsThe vertex quadrangulation QG of a 4-regular graph G visually looks like a graph whose vertices are depicted as empty squares, and the connecting edges are attached to the corners of the squares.
Vladimir R. Rosenfeld
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Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum
Journal of Mathematics, 2021 Let Γ=V,E be a graph. If all the eigenvalues of the adjacency matrix of the graph Γ are integers, then we say that Γ is an integral graph. A graph Γ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper,
Jia-Bao Liu +2 more
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Graph isomorphism and multivariate graph spectrum
Advances in Applied MathematicsWe provide a criterion to distinguish two graphs which are indistinguishable by $2$-dimensional Weisfeiler-Lehman algorithm for almost all graphs. Haemers conjectured that almost all graphs are identified by their spectrum. Our approach suggests that almost all graphs are identified by their generalized block Laplacian spectrum.
Wei Wang, Da Zhao
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On the spectrum of Wenger graphs
Journal of Combinatorial Theory, Series B, 2014 Let $q=p^e$, where $p$ is a prime and $e\geq 1$ is an integer. For $m\geq 1$, let $P$ and $L$ be two copies of the $(m+1)$-dimensional vector spaces over the finite field $\mathbb{F}_q$. Consider the bipartite graph $W_m(q)$ with partite sets $P$ and $L$ defined as follows: a point $(p)=(p_1,p_2,\ldots,p_{m+1})\in P$ is adjacent to a line $[l]=[l_1,l_2,
Cioabă, Sebastian M. +2 more
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Graph-Theoretic Limits of Distributed Computation: Entropy, Eigenvalues, and Chromatic Numbers
EntropyWe address the problem of the distributed computation of arbitrary functions of two correlated sources, X1 and X2, residing in two distributed source nodes, respectively.
Mohammad Reza Deylam Salehi, Derya Malak
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The coalescence of multi-wheel and starlike graphs is DLS [PDF]
Journal of Mahani Mathematical ResearchThe Laplacian spectrum of a graph is obtained by taking the difference of the adjacency spectrum from the diagonal matrix of degrees. If a graph has a unique Laplacian spectrum, it means that it can be identified by this spectrum, it is called $DLS ...
Mohammad Hasan Ahangarani Farahani +1 more
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FEBS Letters, EarlyView.We identified a systemic, progressive loss of protein S‐glutathionylation—detected by nonreducing western blotting—alongside dysregulation of glutathione‐cycle enzymes in both neuronal and peripheral tissues of Taiwanese SMA mice. These alterations were partially rescued by SMN antisense oligonucleotide therapy, revealing persistent redox imbalance as ...
Sofia Vrettou, Brunhilde Wirth
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