1. In-domatic number and some operations in digraphsGermán Benítez-Bobadilla, Laura Pastrana-Ramírez, 2026, izvirni znanstveni članek Opis: Let D be a digraph, a subset S of V(D) is called in-dominating set in D if for each vertex x ∈ V(D) \ S there is a vertex w ∈ S such that (x, w) ∈ A(D). An in-domatic partition of D is a partition of V(D) where all parts are in-dominating sets in D. The maximum number of parts of an in-domatic partition of D is the in-domatic number of D and it is denoted by d⁻(D). In this work, the in-domatic number for some families of digraphs such as complete digraphs, transitive digraphs, directed cycles and the cartesian product of two cycles, is calculated. Also, in-domatically critical digraphs are characterized. Additionally, the in-domatic partitions of the line digraph and some other operations which reflect the adjacency and incidence relations in digraphs are explored.
Ključne besede: in-domatic number, in-domatically critical digraph, line digraph, in-domatically full digraph, cartesian product
Objavljeno v RUP: 21.12.2025; Ogledov: 166; Prenosov: 2
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2. Can Increased Intra-Continental Trade Partnerships Diversify Export Baskets in Africa?Sibusiswe Mchani, Andrew Phiri, 2025, izvirni znanstveni članek Opis: The study investigates the potential of the African Continental Free Trade Area (AfCFTA) agreement in fostering diversified export baskets through increased intra-continental trade partnerships. It aims to evaluate how these trade partnership influence export diversification within Africa. Using network analysis, it develops three indices to measure the degree, closeness, and prestige of trading partners across 54 African countries from 2000 to 2020. These indices, along with traditional estimators, reveal two key findings. Firstly, the quality of trade partnerships, focusing on ‘who’ a country trades with, holds more significance than quantity. Secondly, there is a geographical imbalance, where the effect of trade partnerships turns negative for countries with higher product diversification. In conclusion, while intra-continental trade diversification shows promise, more advanced African nations may experience diminishing returns, suggesting a need for expanding trade networks beyond the continent for sustained export diversification.
Ključne besede: trade partner diversification, product diversification, AFCFTA agreement
Objavljeno v RUP: 18.12.2025; Ogledov: 125; Prenosov: 0
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3. On the wreath product of signed and gain graphs and its spectrumMatteo Cavaleri, Alfredo Donno, Stefano Spessato, 2025, izvirni znanstveni članek Opis: 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.
Ključne besede: gain graph, signed graph, wreath product of graphs, wreath product of groups, circulant gain graph, mixed Kronecker product, π-spectrum
Objavljeno v RUP: 22.10.2025; Ogledov: 360; Prenosov: 5
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4. The 2-rainbow domination number of Cartesian product of cyclesSimon Brezovnik, Darja Rupnik Poklukar, Janez Žerovnik, 2025, izvirni znanstveni članek Opis: A k-rainbow dominating function (kRDF) of G is a function that assigns subsets of {1, 2, ..., k} to the vertices of G such that for vertices v with f(v) = ∅ we have
⋃{u ∈ N(v)}f(u) = {1, 2, ..., k}. The weight w(f) of a kRDF f is defined as
w(f) = ∑{v ∈ V(G)}|f(v)|. The minimum weight of a kRDF of G is called the k-rainbow domination number of G, which is denoted by γrk(G). In this paper, we study the 2-rainbow domination number of the Cartesian product of two cycles. Exact values are given for a number of infinite families and we prove lower and upper bounds for all other cases.
Ključne besede: 2-rainbow domination, domination number, Cartesian product
Objavljeno v RUP: 21.10.2025; Ogledov: 308; Prenosov: 5
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5. Advanced clique algorithms for protein product graphsJanez Konc, Dušanka Janežič, 2025, izvirni znanstveni članek Opis: In this paper, we give a comprehensive overview of the development of clique algo-rithms and their use for drug design based on the search for cliques in protein productgraphs. The maximum clique problem is a computational problem of finding largest sub-sets of vertices in a graph that are all pairwise adjacent. A related problem is the maximumweight clique problem and the highest weight k-clique problem, which both extend the al-gorithm to weighted graphs. The review covers our developed algorithms, starting with ourimproved branch-and-bound algorithm for finding maximum cliques in undirected graphsfrom 2007 up to the recent developments of algorithms for weighted graphs in 2024. Weshow the application of these algorithms to early stages of drug discovery, in particular toprotein binding site detection based on protein similarity search in large protein databasesand to protein-ligand molecular docking.
Ključne besede: cliques, protein product graphs, applications
Objavljeno v RUP: 08.08.2025; Ogledov: 503; Prenosov: 14
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6. Vertex-transitive graphs and their arc-typesMarston D. E. Conder, Tomaž Pisanski, Arjana Žitnik, 2017, izvirni znanstveni članek Opis: Let ▫$X$▫ be a finite vertex-transitive graph of valency ▫$d$▫, and let ▫$A$▫ be the full automorphism group of ▫$X$▫. Then the arc-type of ▫$X$▫ is defined in terms of the sizes of the orbits of the stabiliser ▫$A_v$▫ of a given vertex ▫$v$▫ on the set of arcs incident with ▫$v$▫. Such an orbit is said to be self-paired if it is contained in an orbit ▫$\Delta$▫ of ▫$A$▫ on the set of all arcs of v$X$▫ such that v$\Delta$▫ is closed under arc-reversal. The arc-type of ▫$X$▫ is then the partition of ▫$d$▫ as the sum ▫$n_1 + n_2 + \dots + n_t + (m_1 + m_1) + (m_2 + m_2) + \dots + (m_s + m_s)$▫, where ▫$n_1, n_2, \dots, n_t$▫ are the sizes of the self-paired orbits, and ▫$m_1,m_1, m_2,m_2, \dots, m_s,m_s$▫ are the sizes of the non-self-paired orbits, in descending order. In this paper, we find the arc-types of several families of graphs. Also we show that the arc-type of a Cartesian product of two "relatively prime" graphs is the natural sum of their arc-types. Then using these observations, we show that with the exception of ▫$1+1$▫ and ▫$(1+1)$▫, every partition as defined above is \emph{realisable}, in the sense that there exists at least one vertex-transitive graph with the given partition as its arc-type.
Ključne besede: symmetry type, vertex-transitive graph, arc-transitive graph, Cayley graph, cartesian product, covering graph
Objavljeno v RUP: 03.01.2022; Ogledov: 2974; Prenosov: 26
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