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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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Bounds for the energy of a complex unit gain graph [PDF]
Linear Algebra and Its Applications, 2021 A $\mathbb{T}$-gain graph, $Φ= (G, φ)$, is a graph in which the function $φ$ 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(Φ) $ is defined canonically.
Rajesh Kannan M, Aniruddha Samanta
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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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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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On the determinant of the Laplacian matrix of a complex unit gain graph
Discrete Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yi-Zheng Fan, Shi-Cai Gong
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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 $Φ=(G, φ)$ be a complex unit gain graph (or $\mathbb{T}$-gain graph) and $A(Φ)$ be its adjacency matrix, where $G$ is called the underlying graph of $Φ$. The rank of $Φ$, denoted by $r(Φ)$, is the rank of $A(Φ)$. Denote by $θ(G)=|E(G)|-|V(G)|+ω(G)$ the dimension of cycle spaces of $G$, where $|E(G)|$, $|V(G)|$ and $ω(G)$ are the number of edges ...
Ligong Wang +2 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 $Φ=(G, {\mathbb T}, φ)$ (or $(G, φ)$ for short) consisting of a simple graph $G$, as the underlying graph of $(G, φ)$, the set of unit complex numbers $\mathbb{T}= \{ z \in C:|z|=1 \}$ and a gain function $φ: \overrightarrow{E} \rightarrow \mathbb{T}$ with the property that $φ(e_{i,j})=
Rongxia Hao +2 more
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On the spectrum of complex unit gain graph
Discrete Mathematics, 2019 A $\mathbb{T}$-gain graph is a simple graph in which a unit complex number is assigned to each orientation of an edge, and its inverse is assigned to the opposite orientation. The associated adjacency matrix is defined canonically, and is called $\mathbb{T}$-gain adjacency matrix.
Samanta, Aniruddha, Kannan, M. Rajesh
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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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