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Bounds and extremal graphs for the energy of complex unit gain graphs [PDF]
Linear Algebra and its ApplicationsA complex unit gain graph ($ \mathbb{T} $-gain graph), $ Φ=(G, φ) $ is a graph where the gain function $ φ$ assigns a unit complex number to each orientation of an edge of $ G $ and its inverse is assigned to the opposite orientation. The associated adjacency matrix $ A(Φ) $ is defined canonically. The energy $ \mathcal{E}(Φ) $ of a $ \mathbb{T} $-gain
Aniruddha Samanta, M. Rajesh Kannan
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Balancedness and the Least Laplacian Eigenvalue of Some Complex Unit Gain Graphs
Discussiones Mathematicae Graph Theory, 2020 Let 𝕋4 = {±1, ±i} be the subgroup of 4-th roots of unity inside 𝕋, the multiplicative group of complex units. A complex unit gain graph Φ is a simple graph Γ = (V (Γ) = {v1, . . .
Belardo Francesco +2 more
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A Matrix Approach for Analyzing Signal Flow Graph
Information, 2020 Mason’s gain formula can grow factorially because of growth in the enumeration of paths in a directed graph. Each of the (n − 2)! permutation of the intermediate vertices includes a path between input and output nodes.
Shyr-Long Jeng +2 more
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Density Gain-Rate Peaks for Spectral Clustering
IEEE Access, 2021 Clustering has been troubled by varying shapes of sample distributions, such as line and spiral shapes. Spectral clustering and density peak clustering are two feasible techniques to address this problem, and have attracted much attention from academic ...
Jiexing Liu, Chenggui Zhao
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Line graphs of complex unit gain graphs with least eigenvalue -2
The Electronic Journal of Linear Algebra, 2021 Let $\mathbb T$ be the multiplicative group of complex units, and let $\mathcal L (\Phi)$ denote a line graph of a $\mathbb{T}$-gain graph $\Phi$. Similarly to what happens in the context of signed graphs, the real number $\min Spec(A(\mathcal L (\Phi))$, that is, the smallest eigenvalue of the adjacency matrix of $\mathcal L(\Phi)$, is not less than $-
Maurizio Brunetti, Francesco Belardo
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Coloring permutation-gain graphs
Contributions to Discrete Mathematics, 2021 Correspondence colorings of graphs were introduced in 2018 by Dvořák and Postle as a generalization of list colorings of graphs which generalizes ordinary graph coloring. Kim and Ozeki observed that correspondence colorings generalize various notions of signed-graph colorings which again generalizes ordinary graph colorings.
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New Journal of Physics, 2021 Non-Hermitian (NH) topological states, such as the doubly-degenerate nodes dubbed as exceptional points (EPs) in Bloch band structure of 2D lattices driven by gain and loss, have attracted much recent interest.
Hang Liu, Sheng Meng, Feng Liu
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Matroids of Gain Graphs in Applied Discrete Geometry [PDF]
Transactions of the American Mathematical Society, 2012 A Γ \Gamma -gain graph is a graph whose oriented edges are labeled invertibly from a group Γ \Gamma . Zaslavsky proposed two matroids associated with Γ \Gamma -gain graphs, called frame matroids and lift matroids, and investigated linear representations of them.
Shin‐ichi Tanigawa
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Certain operations on interval-valued picture fuzzy graphs with application
International Journal of Mathematics for Industry, 2023 Graph theory has various applications in computer science, such as image segmentation, clustering, data mining, image capturing, and networking. Fuzzy graph (FG) theory has been widely adopted to handle uncertainty in graph-related problems.
Biswajit Das Adhikari +3 more
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Applied Artificial Intelligence, 2023 Graph convolution neural networks have shown powerful ability in recommendation, thanks to extracting the user-item collaboration signal from users’ historical interaction information.
Yang Li +4 more
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