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On the wreath product of signed and gain graphs and its spectrum
Matteo Cavaleri, Alfredo Donno, Stefano Spessato, 2025, original scientific article

Abstract: We introduce a notion of wreath product of two gain graphs (Γ_1, ψ_1, G_1) and (Γ_2, ψ_2, G_2), producing a gain graph over the direct product group G_2|V_Γ1| × G_1, whose underlying graph is the classical wreath product of graphs Γ_1≀Γ_2. By composition with a suitable group homomorphism, our construction produces a signed graph when the two factors are signed graphs. We prove that the wreath product is stable under switching isomorphism. By using group representations, we are able to perform spectral computations on the wreath product: in particular, we determine its largest and its smallest eigenvalue, and we give a description of the spectrum when the first factor is a complex unit complete balanced or antibalanced gain graph, and the second factor is circulant. Finally, when G_1 is a group of permutations of the vertex set of the first factor, and the group G_2 is abelian, we give an alternative definition producing a gain graph over the group wreath product G_1≀G_2, which turns out to be stable under switching equivalence of the second factor, when the first factor is balanced.
Keywords: gain graph, signed graph, wreath product of graphs, wreath product of groups, circulant gain graph, mixed Kronecker product, π-spectrum
Published in RUP: 22.10.2025; Views: 348; Downloads: 5
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On the notion of duals of certain AB functions
Amar Bapić, Enes Pašalić, Samir Hodžić, 2019, published scientific conference contribution

Keywords: vectorial bent functions, AB functions, Dual functions, Walsh spectrum
Published in RUP: 18.10.2021; Views: 2291; Downloads: 28
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On a version of the spectral excess theorem
Miquel Àngel Fiol, Safet Penjić, 2020, original scientific article

Keywords: adjacency algebra, spectrum, distance-regular graph, Laplacian
Published in RUP: 02.12.2020; Views: 4269; Downloads: 39
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Cyclic carbon polyynes
Lorentz Jäntschi, Sorana D. Bolboacǎ, Dušanka Janežič, 2016, independent scientific component part or a chapter in a monograph

Keywords: cyclic polyynes, theoretical IR spectrum, density functional theory calculation
Published in RUP: 18.03.2020; Views: 4145; Downloads: 60
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On distance integral graphs
Milan Pokorný, Pavel Híc, Dragan Stevanović, Marko Milošević, 2015, original scientific article

Keywords: distance spectrum, distance integral graph, tree, complete split graph
Published in RUP: 03.04.2017; Views: 4323; Downloads: 146
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