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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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Matroids of Gain Signed Graphs [PDF]
Discrete & Computational Geometry, 2022 13 fig., 46 pp. v2 has new Example 3.7, minor editing, 47 pp.
Laura N. Anderson +2 more
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Gain distance matrices for complex unit gain graphs [PDF]
Discrete Mathematics, 2021 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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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 $-
Maurizio Brunetti, Francesco Belardo
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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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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.
Daniel Slilaty
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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 $G$. For instance, for two signed graphs, this notion of cospectrality is equivalent to the cospectrality of their signed adjacency ...
Matteo Cavaleri +2 more
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Multi-duplicated Characterization of Graph Structures using Information Gain Ratio for Graph Neural Networks [PDF]
IEEE Access, 2022 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 features of neighboring nodes. However, they fail to directly characterize and leverage the structural information. In this paper, we propose multi-duplicated
Yuga Oishi, Ken kaneiwa
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GAIN: Graph Attention & Interaction Network for Inductive Semi-Supervised Learning over Large-scale Graphs [PDF]
IEEE Transactions on Knowledge and Data Engineering, 2020 Accepted by IEEE Transactions on Knowledge and Data Engineering (TKDE)
Yunpeng Weng +3 more
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