On cospectrality of gain graphs [PDF]
Special Matrices, 2022 We define GG-cospectrality of two GG-gain graphs (Γ,ψ)\left(\Gamma ,\psi ) and (Γ′,ψ′)\left(\Gamma ^{\prime} ,\psi ^{\prime} ), proving that it is a switching isomorphism invariant.
Cavaleri Matteo, Donno Alfredo
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On two Laplacian matrices for skew gain graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2021 Gain graphs are graphs where the edges are given some orientation and labeled with the elements (called gains) from a group so that gains are inverted when we reverse the direction of the edges.
Roshni T. Roy +2 more
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NEPS of complex unit gain graphs
The Electronic Journal of Linear Algebra, 2023 A complex unit gain graph (or $\mathbb T$-gain graph) is a gain graph with gains in $\mathbb T$, the multiplicative group of complex units. Extending a classical construction for simple graphs due to Cvektovic, suitably defined noncomplete extended $p ...
Francesco Belardo +2 more
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Eigenvalues of complex unit gain graphs and gain regularity [PDF]
Special MatricesA complex unit gain graph (or T{\mathbb{T}}-gain graph) Γ=(G,γ)\Gamma =\left(G,\gamma ) is a gain graph with gains in T{\mathbb{T}}, the multiplicative group of complex units.
Brunetti Maurizio
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On the adjacency matrix of a complex unit gain graph [PDF]
Linear and Multilinear Algebra, 2018 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.
Ranjit Mehatari +2 more
semanticscholar +7 more sources
Multi-Duplicated Characterization of Graph Structures Using Information Gain Ratio for Graph Neural Networks [PDF]
IEEE Access, 2023 Various graph neural networks (GNNs) have been proposed to solve node classification tasks in machine learning for graph data. GNNs use the structural information of graph data by aggregating the feature vectors of neighboring nodes.
Yuga Oishi, Ken Kaneiwa
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Line and Subdivision Graphs Determined by
Mathematics, 2019 Let T 4 = { ± 1 , ± i } be the subgroup of fourth roots of unity inside T , the multiplicative group of complex units. For a T 4 -gain graph Φ = ( Γ , T 4 , φ ) , we introduce gain functions on ...
Abdullah Alazemi +4 more
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Normalized Laplacians for gain graphs [PDF]
The American Journal of Combinatorics, 2022 We propose the notion of normalized Laplacian matrix $\mathcal{L}(\Phi)$ for a gain graph $\Phi$ and study its properties in detail, providing insights and counterexamples along the way.
M. Rajesh Kannan +2 more
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Spectral properties of complex unit gain graphs [PDF]
Linear Algebra and its Applications, 2012 13 pages, 1 figure, to appear in Linear Algebra ...
Nathan Reff
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Bounds and extremal graphs for the energy of complex unit gain graphs [PDF]
Linear Algebra and its Applications, 2023 A 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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