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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Eigenvalues of complex unit gain graphs and gain regularity
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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Gain distance matrices for complex unit gain graphs
Discrete Mathematics, 2022 A complex unit gain graph ($ \mathbb{T} $-gain graph), $ =(G, ) $ is a graph where the function $ $ assigns a unit complex number to each orientation of an edge of $ G $, and its inverse is assigned to the opposite orientation. %A complex unit gain graph($ \mathbb{T} $-gain graph) is a simple graph where each orientation of an edge is given a ...
Aniruddha Samanta, M. Rajesh Kannan
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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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Short-Term Nationwide Airport Throughput Prediction With Graph Attention Recurrent Neural Network
Frontiers in Artificial Intelligence, 2022 With the dynamic air traffic demand and the constrained capacity resources, accurately predicting airport throughput is essential to ensure the efficiency and resilience of air traffic operations.
Xinting Zhu +6 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 $p$-sums (NEPS, for short) of $\mathbb T$-gain graphs are considered in this paper. Structural properties
Francesco Belardo +2 more
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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 $-
Belardo F., Brunetti M.
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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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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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Spectral properties of complex unit gain graphs [PDF]
Linear Algebra and its Applications, 2012 13 pages, 1 figure, to appear in Linear Algebra ...
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