Results 1 to 10 of about 176,464 (158)
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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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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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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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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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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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 determinant of the Laplacian matrix of a quaternion unit gain graph
Discrete Mathematics16 pages, 1 ...
Ivan Kyrchei
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Characterizations of line graphs in signed and gain graphs [PDF]
European Journal of Combinatorics, 2022 We generalize three classical characterizations of line graphs to line graphs of signed and gain graphs: the Krausz's characterization, the van Rooij and Wilf's characterization and the Beineke's characterization. In particular, we present a list of forbidden gain subgraphs characterizing the class of gain-line graphs.
Matteo Cavaleri +2 more
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Gain distance matrices for complex unit gain graphs
Discrete Mathematics, 2022 20 pages; 2 ...
Aniruddha Samanta, M. Rajesh Kannan
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