1. A note on Cayley nut graphs whose degree is divisible by fourIvan Damnjanović, 2026, original scientific article Abstract: A nut graph is a nontrivial simple graph such that its adjacency matrix has a one-dimensional null space spanned by a full vector. Fowler et al. in 2020 proved that there is a d-regular vertex-transitive nut graph of order n only if 4 ∣ d, 2 ∣ n, n ≥ d + 4 or d≡₄2, 4 ∣ n and n ≥ d + 6. It was recently shown that there exists a d-regular circulant nut graph of order n if and only if 4 ∣ d, 2 ∣ n, d > 0, together with n ≥ d + 4 if d≡₈4 and n ≥ d + 6 if 8 ∣ d, as well as (n, d) ≠ (16, 8) (in the paper from 2024). In this paper, we demonstrate the existence of a d-regular Cayley nut graph of order n for each n and d with 4 ∣ d, d > 0 and 2 ∣ n, n ≥ d + 4, thereby finding all the orders attainable by a Cayley nut graph, or vertex-transitive nut graph, with a fixed degree divisible by four.
Keywords: nut graph, Cayley graph, vertex-transitive graph, circulant graph, graph spectrum, graph eigenvalue
Published in RUP: 23.03.2026; Views: 314; Downloads: 4
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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: 2032; Downloads: 28
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3. On minimal forbidden subgraphs for the class of EDM-graphsGašper Jaklič, Jolanda Modic, 2015, original scientific article Abstract: In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. Graphs, for which the distance matrix is not an EDM (NEDM-graphs), are studied. All simple connected non-isomorphic graphs on ▫$n \le 8$▫ nodes are analysed and a characterization of the smallest NEDM-graphs, i.e., the minimal forbidden subgraphs, is given. It is proven that bipartite graphs and some subdivisions of the smallest NEDM-graphs are NEDM-graphs, too.
Keywords: graph theory, graph, Euclidean distance matrix, distance, eigenvalue
Published in RUP: 31.12.2021; Views: 2679; Downloads: 23
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5. Bifurkacije ravnovesnih stanj vektorskih polj in uporaba v sistemih plenilec-plen : zaključna nalogaRade Nježić, 2018, undergraduate thesis Keywords: dynamical system, differential equation, equilibrium, local stability, bifurcation, eigenvalue, mathematical model, predator, prey
Published in RUP: 17.09.2018; Views: 3848; Downloads: 44
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6. Določeni razredi (hiper)grafov in njihove algebraične lastnosti : doktorska disertacijaPaweł Petecki, 2016, doctoral dissertation Keywords: hypergraph, hamiltonian cycle, decomposition, double generalized Petersen graph, automorphism group, vertex-transitive, sign graph, L-eigenvalue, lollipop graph
Published in RUP: 09.08.2016; Views: 5283; Downloads: 38
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7. On graphs whose Laplacian index does not exceed 4.5JianFeng Wang, Francesco Belardo, Qiongxiang Huang, Enzo M. Li Marzi, 2013, original scientific article Keywords: lastna vrednost, Laplacova matrika, grafi, eigenvalue, Laplacian matrix, graphs
Published in RUP: 15.10.2015; Views: 5706; Downloads: 181
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8. Adjacency preservers, symmetric matrices, and coresMarko Orel, 2012, original scientific article Abstract: It is shown that the graph ▫$\Gamma_n$▫ that has the set of all ▫$n \times n$▫ symmetric matrices over a finite field as the vertex set, with two matrices being adjacent if and only if the rank of their difference equals one, is a core if ▫$n \ge 3$▫. Eigenvalues of the graph ▫$\Gamma_n$▫ are calculated as well.
Keywords: adjacency preserver, symmetric matrix, finite field, eigenvalue of a graph, coloring, quadratic form
Published in RUP: 15.10.2013; Views: 5986; Downloads: 150
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