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Complex unit gain graphs of rank 2
Linear Algebra and its Applications, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng Xu +3 more
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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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On the adjacency matrix of a complex unit gain graph [PDF]
Linear and Multilinear Algebra, 2020 A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge. In this article, first we establish bounds for the eigenvalues of the complex unit gain graphs.
Ranjit Mehatari +2 more
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Bounds for the energy of a complex unit gain graph [PDF]
Linear Algebra and its Applications, 2021 A $\mathbb{T}$-gain graph, $ = (G, )$, is a graph in which the function $ $ assigns a unit complex number to each orientation of an edge, and its inverse is assigned to the opposite orientation. The associated adjacency matrix $ A( ) $ is defined canonically.
Aniruddha Samanta, M. Rajesh Kannan
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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 Properties of Dual Unit Gain Graphs [PDF]
SymmetryIn this paper, we study dual quaternion, dual complex unit gain graphs, and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and
Chunfeng Cui +3 more
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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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Godsil-McKay switchings for gain graphs [PDF]
The Electronic Journal of Linear Algebra, 2022 We introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of $G$-cospectral gain graphs, that are gain graphs cospectral with respect to every representation of the gain group $G$.
Matteo Cavaleri +2 more
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F1000Research, 2019 Metagenomic sequencing is an increasingly common tool in environmental and biomedical sciences. While software for detailing the composition of microbial communities using 16S rRNA marker genes is relatively mature, increasingly researchers are ...
Mike W.C. Thang +4 more
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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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