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2. On the BCI problemTed Dobson, Gregory Robson, 2026, izvirni znanstveni članek Opis: Let G be a group. The BCI problem asks whether two Haar graphs of G are isomorphic if and only if they are isomorphic by an element of an explicit list of isomorphisms. We first generalize this problem in a natural way and give a theoretical way to solve the isomorphism problem for the natural generalization. We then restrict our attention to abelian groups and, with an exception, reduce the problem to the isomorphism problem for a related quotient, component, or corresponding Cayley digraph. For Haar graphs of an abelian group of odd order with connection sets S those of Cayley graphs (i.e. S = -S), the exception does not exist. For Haar graphs of cyclic groups of odd order with connection sets those of a Cayley graph, among others, we solve the isomorphism problem.
Ključne besede: Cayley, Haar, CI, BCI, abelian group
Objavljeno v RUP: 17.08.2026; Ogledov: 20; Prenosov: 1
 Celotno besedilo (511,43 KB) |
3. Irregular graph labelings in Abelian groupsSylwia Cichacz, 2026, izvirni znanstveni članek Opis: Let G⃗ = (V,E) be a directed graph of order n. If there exists a mapping ψ from E(G⃗) to an Abelian group Γ such that if we define a mapping φ_ψ from V(G⃗) to Γ by
φ_ψ(x) = ∑y ∈ N⁺(x)ψ(xy) − ∑y ∈ N⁻(x)ψ(yx), (x ∈ V(G⃗)), then φψ is injective, then such a labeling ψ is called Γ-irregular.
Recently it was showed that if n is large enough then G⃗ has a Γ-irregular labeling for any Γ such that |Γ| > (1 + ε)n (in the paper from Cichacz and Tuza from 2022). In this paper, we prove that if all weakly connected components of G⃗ are of size at least 4, then G⃗ has a Γ-irregular labeling for any finite group Γ such that |Γ| >= n + 5.
Ključne besede: finite Abelian group, directed graph, zero-sum sets
Objavljeno v RUP: 11.08.2026; Ogledov: 107; Prenosov: 1
Celotno besedilo (331,17 KB) |
4. Group distance magic cubic graphsSylwia Cichacz, Štefko Miklavič, 2026, izvirni znanstveni članek Opis: A $\Gamma$-distance magic labeling of a graph $G = (V, E)$ with $|V| = n$ is a bijection $\ell$ from $V$ to an Abelian group $\Gamma$ of order $n$, for which there exists $\mu \in \Gamma$, such that the weight $w(x) =\sum_{y\in N(x)}\ell(y)$ of every vertex $x \in V$ is equal to $\mu$. In this case, the element $\mu$ is called the magic constant of $G$. A graph $G$ is called a group distance magic if there exists a $\Gamma$-distance magic labeling of $G$ for every Abelian group $\Gamma$ of order $n$. In this paper, we focused on cubic $\Gamma$-distance magic graphs as well as some properties of such graphs.
Ključne besede: group distance magic labeling, Kotzig array, generalized Petersen graph
Objavljeno v RUP: 06.05.2026; Ogledov: 521; Prenosov: 9
Celotno besedilo (187,65 KB)
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5. Automorphisms and quotients of 2-colored quasi best match graphsAnnachiara Korchmaros, 2026, izvirni znanstveni članek Opis: 2-colored quasi best match graphs (2-qBMGs) are directed graphs that arose in evolution theory. Investigations of 2-qBMGs have mostly focused on computational issues. However, 2-qBMGs also have relevant properties for structural graph theory; in particular, their undirected underlying graph is free from induced paths and cycles of size at least 6. In this paper, results on the structure of the automorphism groups of 2-qBMGs are obtained, which shows how to construct 2-qBMGs with large automorphism groups.
Ključne besede: group of automorphisms, bipartite graphs, phylogenetics
Objavljeno v RUP: 05.01.2026; Ogledov: 1442; Prenosov: 4
Celotno besedilo (498,12 KB) |
6. Platonic configurations of points and linesJurij Kovič, Aleksander Simonič, 2026, izvirni znanstveni članek Opis: We present some methods for constructing connected spatial geometric configurations (p_q, n_k) of points and lines, preserved by the same isometries of Euclidean space E³ as the predetermined Platonic solid. In this paper, we are mainly interested in configurations (n₃), (n₄), and (n₅), but also in unbalanced configurations (p₃, n₄), (p₃, n₅), and (p₄, n₅).
Ključne besede: configuration of points and lines, symmetry group, Platonic solid, centrally symmetric solid, projection from a point
Objavljeno v RUP: 22.12.2025; Ogledov: 639; Prenosov: 3
Celotno besedilo (533,56 KB) |
7. Nut graphs with a given automorphism groupNino Bašić, Patrick W. Fowler, 2025, izvirni znanstveni članek Opis: A nut graph is a simple graph of order 2 or more for which the adjacency matrix has a single zero eigenvalue such that all nonzero kernel eigenvectors have no zero entry (i.e. are full). It is shown by construction that every finite group can be represented as the group of automorphisms of infinitely many nut graphs. It is further shown that such nut graphs exist even within the class of regular graphs; the cases where the degree is 8, 12, 16, 20 or 24 are realised explicitly.
Ključne besede: nut graph, graph automorphism, automorphism group, nullity, graph spectra, f-universal
Objavljeno v RUP: 25.11.2025; Ogledov: 1152; Prenosov: 5
Celotno besedilo (526,71 KB)
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8. A unified Erdős–Pósa theorem for cycles in graphs labelled by multiple abelian groupsJ. Pascal Gollin, Kevin Hendrey, O-joung Kwon, Sang-il Oum, Youngho Yoo, 2025, izvirni znanstveni članek Opis: In 1965, Erdős and Pósa proved that there is an (approximate) duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold for odd cycles, and Dejter and Neumann-Lara asked in 1988 to find all pairs (l, z) of integers where such a duality holds for the family of cycles of length l modulo z. We characterise all such pairs, and we further generalise this characterisation to cycles in graphs labelled with a bounded number of abelian groups, whose values avoid a bounded number of elements of each group. This unifies almost all known types of cycles that admit such a duality, and it also provides new results. Moreover, we characterise the obstructions to such a duality in this setting, and thereby obtain an analogous characterisation for cycles in graphs embeddable on a fixed compact orientable surface.
Ključne besede: Erdős-Pósa property, cycle packing, group-labelled graph
Objavljeno v RUP: 17.11.2025; Ogledov: 997; Prenosov: 10
Celotno besedilo (1,17 MB)
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9. Regular maps with primitive automorphism groupsGareth A. Jones, Martin Mačaj, 2025, izvirni znanstveni članek Opis: We classify the regular maps ℳ which have automorphism groups G acting faithfully and primitively on their vertices. As a permutation group G must be of almost simple or affine type, with dihedral point stabilisers. We show that all such almost simple groups, namely all but a few groups PSL2(q), PGL2(q) and Sz(q), arise from regular maps, which are always non-orientable. In the affine case, the maps ℳ occur in orientable and non-orientable Petrie dual pairs. We give the number of maps associated with each group, together with their genus and extended type. Some of this builds on earlier work of the first author on generalised Paley maps, and on recent work of Jajcay, Li, Širáň and Wang on maps with quasiprimitive automorphism groups.
Ključne besede: regular map, automorphism group, primitive, almost simple, affine group
Objavljeno v RUP: 04.11.2025; Ogledov: 925; Prenosov: 6
Celotno besedilo (512,34 KB) |
10. Transitive regular q-analogs of graphsDean Crnković, Vedrana Mikulić Crnković, Andrea Švob, Matea Zubović Žutolija, 2025, izvirni znanstveni članek Opis: In 1976, Delsarte introduced the notion of q-analogs of designs, and q-analogs of graphs were introduced recently by M. Braun et al. In this paper, we extend that study by giving a method for constructing transitive regular q-analogs of graphs. Further, we illustrate the method by giving some examples. Additionally, we introduced the notion of q-analogs of quasi-strongly regular graphs and give examples of transitive q-analogs of quasi-strongly regular graphs coming from spreads.
Ključne besede: q-ary design, q-ary graph, regular graph, transitive group
Objavljeno v RUP: 03.11.2025; Ogledov: 723; Prenosov: 6
Celotno besedilo (382,29 KB) |
