Results 11 to 20 of about 39,210 (193)
The rank of a complex unit gain graph in terms of the matching number [PDF]
Linear Algebra and its Applications, 2020 A complex unit gain graph (or ${\mathbb T}$-gain graph) is a triple $ =(G, {\mathbb T}, )$ (or $(G, )$ for short) consisting of a simple graph $G$, as the underlying graph of $(G, )$, the set of unit complex numbers $\mathbb{T}= \{ z \in C:|z|=1 \}$ and a gain function $ : \overrightarrow{E} \rightarrow \mathbb{T}$ with the property that $ (e_{
Shengjie He, Rong-Xia Hao, Fengming Dong
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The rank of a complex unit gain graph in terms of the rank of its underlying graph [PDF]
Journal of Combinatorial Optimization, 2019 Let $ =(G, )$ be a complex unit gain graph (or $\mathbb{T}$-gain graph) and $A( )$ be its adjacency matrix, where $G$ is called the underlying graph of $ $. The rank of $ $, denoted by $r( )$, is the rank of $A( )$. Denote by $ (G)=|E(G)|-|V(G)|+ (G)$ the dimension of cycle spaces of $G$, where $|E(G)|$, $|V(G)|$ and $ (G)$ are the number of
Yong Lu, Ligong Wang, Qiannan Zhou
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On the determinant of the Laplacian matrix of a complex unit gain graph
Discrete Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Yi, Gong, Shi-Cai, Fan, Yi-Zheng
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Unit gain graphs with two distinct eigenvalues and systems of lines in complex space
Discrete Mathematics, 2022 Since the introduction of the Hermitian adjacency matrix for digraphs, interest in so-called complex unit gain graphs has surged. In this work, we consider gain graphs whose spectra contain the minimum number of two distinct eigenvalues. Analogously to graphs with few distinct eigenvalues, a great deal of structural symmetry is required for a gain ...
Wissing, Pepijn, van Dam, Edwin R.
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On eigenspaces of some compound complex unit gain graphs
, 2021 Summary: Let \(\mathbb{T}\) be the multiplicative group of complex units, and let \(L(\Phi)\) denote the Laplacian matrix of a nonempty \(\mathbb{T}\)-gain graph \(\Phi = (\Gamma, \mathbb{T}, \gamma)\). The gain line graph \(\mathcal{L}(\Phi)\) and the gain subdivision graph \(\mathcal{S}(\Phi)\) are defined up to switching equivalence.
Belardo F., Brunetti M.
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Inertia indices of a complex unit gain graph in terms of matching number
Linear and Multilinear Algebra, 2022 A complex unit gain graph is a triple $ =(G, \mathbb{T}, )$ (or $G^ $ for short) consisting of a simple graph $G$, as the underlying graph of $G^ $, the set of unit complex numbers $\mathbb{T}={z\in \mathbb{C}: |z| = 1}$ and a gain function $ : \overrightarrow{E}\rightarrow \mathbb{T}$ such that $ (e_{i,j})= (e_{j,i}) ^{-1}$.
Lu, Yong, Wu, Qi
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Bounds for the rank of a complex unit gain graph in terms of the independence number [PDF]
Linear and Multilinear Algebra, 2020 arXiv admin note: substantial text overlap with arXiv:1907.07837, arXiv:1909 ...
He, Shengjie, Hao, Rong-Xia, Yu, Aimei
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Spectral Characterizations of Complex Unit Gain Graphs
, 2022 While eigenvalues of graphs are well studied, spectral analysis of complex unit gain graphs is still in its infancy. This thesis considers gain graphs whose gain groups are gradually less and less restricted, with the ultimate goal of classifying gain graphs that are characterized by their spectra. In such cases, the eigenvalues of a gain graph contain
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FEBS Letters, EarlyView.In this study, we found that human cervical‐derived adipocytes maintain intracellular iron level by regulating the expression of iron transport‐related proteins during adrenergic stimulation. Melanotransferrin is predicted to interact with transferrin receptor 1 based on in silico analysis.
Rahaf Alrifai +9 more
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Tau acetylation at K331 has limited impact on tau pathology in vivo
FEBS Letters, EarlyView.We mapped tau post‐translational modifications in humanized MAPT knock‐in mice and in amyloid‐bearing double knock‐in mice. Acetylation within the repeat domain, particularly around K331, showed modest increases under amyloid pathology. To test functional relevance, we generated MAPTK331Q knock‐in mice.
Shoko Hashimoto +3 more
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