Results 1 to 10 of about 168,521 (260)
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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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.
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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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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Gain distance matrices for complex unit gain graphs
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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Matroids of Gain Signed Graphs
Discrete & Computational Geometry, 2023 13 fig., 46 pp. v2 has new Example 3.7, minor editing, 47 pp.
Laura Anderson +2 more
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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.
Cavaleri, Matteo +2 more
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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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