1. On the wreath product of signed and gain graphs and its spectrumMatteo 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: 446; Downloads: 5
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2. Exploring the bounds and relationships of chemical graph indices : master's thesisArbër Avdullahu, 2023, master's thesis Keywords: energy of a graph, Randić index, first Zagreb index, IRB index, extremal graph, spectrum, eigenvalue, metaheuristic
Published in RUP: 05.10.2023; Views: 1782; Downloads: 13
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6. Connected graphs of fixed order and size with minimal index : structural considerationsSlobodan Simić, Enzo M. Li Marzi, Francesco Belardo, 2004, original scientific article Keywords: spekter grafa, največja lastna vrednost, spektralni radij, indeks grafa, graph spectrum, largest eingenvalue, spectral radius, graph index, nested split graphs
Published in RUP: 15.10.2015; Views: 5110; Downloads: 63
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7. Large sets of long distance equienergetic graphsDragan Stevanović, 2009, original scientific article Abstract: Distance energy of a graph is a recent energy-type invariant, defined as the absolute deviation of the eigenvalues of the distance matrix of the graph. Two graphs of the same order are said to be distance equienergetic if they have equal distance energy, while they have distinct spectra of their distance matrices. Examples of pairs of distance equienergetic graphs appear in the literature already, but most of them have diameter two only. We describe here the distance spectrum of a special composition of regular graphs, and, as an application, we show that for any ▫$n \ge 3$▫, there exists a set of ▫$n + 1$▫ distance equienergetic graphs which have order ▫$6n$▫ and diameter ▫$n - 1$▫ each.
Keywords: graph theory, distance spectrum, distance energy, join, regular graphs
Published in RUP: 15.10.2013; Views: 6855; Downloads: 152
Full text (144,63 KB) |
