20.500.12556/RUP-22013 On the wreath product of signed and gain graphs and its spectrum Venčni produkt predznačenih grafov in grafov ojačenja in njegov spekter 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. gain graph signed graph wreath product of graphs wreath product of groups circulant gain graph mixed Kronecker product π-spectrum graf ojačenja predznačeni graf venčni produkt grafov venčni produkt grup cirkulantni graf ojačenja mešani Kroneckerjev produkt π-spekter true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-10-22 13:28:46 2025-10-22 13:28:46 2025-11-14 03:05:50 0000-00-00 00:00:00 2025 0 0 30 str. no. 3, [article no.] P3.10 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-06-20 519.17 1855-3974 https://doi.org/10.26493/1855-3974.3332.d9b AMC_Cavaleri,Donno,Spessato_2025.pdf AMC_Cavaleri,Donno,Spessato_2025.pdf 1 E6C9CC269ED846A0459BC6A733AEB459 efdee8dc5915c3e9aafa8f00f754c371acb9fa36d63f650f575d41a5c0c1e914 2301dac9-af3b-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31948 Založba Univerze na Primorskem 0 0 0