Results 11 to 20 of about 319,037 (217)
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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Symmetry in complex unit gain graphs and their spectra
Linear Algebra and its ApplicationsComplex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respective relations to one-another. Our main result is a construction that transforms an arbitrary complex unit gain graph into infinitely many switching-distinct ones whose ...
Pepijn Wissing, Edwin R. van Dam
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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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Modelling of Path Arrival Rate for In-Room Radio Channels with Directive Antennas [PDF]
, 2017 We analyze the path arrival rate for an inroom radio channel with directive antennas. The impulse response of this channel exhibits a transition from early separate components followed by a diffuse reverberation tail.
Pedersen, Troels
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Fitting a geometric graph to a protein-protein interaction network [PDF]
, 2008 Finding a good network null model for protein-protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution.
Barabási +46 more
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Spatial networks with wireless applications [PDF]
, 2018 Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network.
Dettmann, Carl +2 more
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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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