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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. We establish bounds for the eigenvalues of \(\mathcal{L}(\Phi)\
M. Rajesh Kannan +2 more
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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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On cospectrality of gain graphs
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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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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Gain and Pain in Graph Partitioning: Finding Accurate Communities in Complex Networks [PDF]
AlgorithmsThis paper presents an approach to community detection in complex networks by simultaneously incorporating a connectivity-based metric and Max-Min Modularity.
Arman Ferdowsi, Maryam Dehghan Chenary
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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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Burnside Chromatic Polynomials of Group-Invariant Graphs
Discussiones Mathematicae Graph Theory, 2023 We introduce the Burnside chromatic polynomial of a graph that is invariant under a group action. This is a generalization of the Q-chromatic function Zaslavsky introduced for gain graphs.
White Jacob A.
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Domain Entity Extraction Method Based on Graph Sorting and Maximal Information Gain [PDF]
Jisuanji gongcheng, 2022 Domain knowledge graphs play an important role in various industries, and the acquisition of the domain entity is an important basis for their construction.However, existing approaches frequently rely on human work such as data annotation and the ...
ZHANG Xiaoming, ZHENG Lixin, WANG Huiyong
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On the Fractionalization of the Shift Operator on Graphs
IEEE Access, 2022 The theory of graph signal processing has been established with the purpose of generalizing tools from classical digital signal processing to the cases where the signal domain can be modeled by an arbitrary graph.
Guilherme B. Ribeiro +2 more
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