Results 21 to 30 of about 3,672,970 (235)
Gain distance matrices for complex unit gain graphs [PDF]
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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Information Gain Propagation: a new way to Graph Active Learning with Soft Labels [PDF]
International Conference on Learning Representations, 2022 Graph Neural Networks (GNNs) have achieved great success in various tasks, but their performance highly relies on a large number of labeled nodes, which typically requires considerable human effort.
Wentao Zhang +7 more
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Symmetry in complex unit gain graphs and their spectra
Linear Algebra and its Applications, 2023 Complex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respective relations to one-another. Our main result is a construction that transforms an arbitrary complex unit gain graph into infinitely many switching-distinct ones whose ...
Pepijn Wissing, Edwin R. van Dam
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Oriented gain graphs, line graphs and eigenvalues [PDF]
Linear Algebra and its Applications, 2016 A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of gain graphs with complex units, matrix properties are established.
Nathan Reff
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A switching method for constructing cospectral gain graphs
Discrete Mathematics, 2023 A gain graph over a group $G$, also referred to as $G$-gain graph, is a graph where an element of a group $G$, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a generalization of signed graphs, among others.
Abiad, Aida +2 more
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A group representation approach to balance of gain graphs [PDF]
Journal of Algebraic Combinatorics, 2020 We study the balance of $G$-gain graphs, where $G$ is an arbitrary group, by investigating their adjacency matrices and their spectra. As a first step, we characterize switching equivalence and balance of gain graphs in terms of their adjacency matrices in $M_n(\mathbb C G)$.
Matteo Cavaleri +2 more
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Bounds for the rank of a complex unit gain graph in terms of the independence number [PDF]
Linear and multilinear algebra, 2019 A complex unit gain graph (or -gain graph) is a triple (or for short) consisting of a simple graph G with , as the underlying graph of , the set of unit complex numbers and a gain function with the property that . The adjacency matrix of is , where if is
Shengjie He, Rongxia Hao, A. Yu
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Gain distance Laplacian matrices for complex unit gain graphs [PDF]
18 pages, 1 ...
Suliman Khan
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Modeling sleep modes gains with random graphs [PDF]
2011 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), 2011 Nowadays two main approaches are being pursued to reduce energy consumption of network devices: the use of sleep modes in which devices can be put in low-power state, and the adoption of energy proportional approaches where the device architecture is designed to make energy consumption proportional to the actual load.
CHIARAVIGLIO, LUCA +3 more
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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, 2017 Let Φ=(G,φ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi =(G ...
Yong Lu, Ligong Wang, Qiannan Zhou
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