1. Mutual-visibility and general position sets in Sierpiński triangle graphsDanilo Korže, Aleksander Vesel, 2025, izvirni znanstveni članek Opis: For a given graph G, the general position problem asks for the largest size of a set of vertices M ⊆ V(G) such that no three distinct vertices of M belong to a common shortest path in G. A relaxation of this concept is based on the condition that two vertices x, y ∈ V(G) are M-visible, meaning there exists a shortest x, y-path in G that does not pass through any vertex of M \ {x, y}. If every pair of vertices in M is M-visible, then M is called a mutual-visibility set of G. The cardinality of the largest mutual-visibility set of G is called the mutual-visibility number of G. Some wellknown variations of this concept consider the total, outer, and dual mutual-visibility sets of a graph. We present results on the general position problem and the various mutual-visibility problems in Sierpi ´nski triangle graphs.
Ključne besede: general position, mutual visibility, Sierpinski triangle graph
Objavljeno v DKUM: 29.05.2025; Ogledov: 0; Prenosov: 0
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2. 2-rainbow independent domination in complementary prismsDragana Božović, Gordana Radić, Aleksandra Tepeh, 2025, izvirni znanstveni članek Opis: A function f that assigns values from the set to each vertex of a graph G is called a 2-rainbow independent dominating function, if the vertices assigned the value 1 form an independent set, the vertices assigned the value 2 form another independent set, and every vertex to which 0 is assigned has at least one neighbor in each of the mentioned independent sets. The weight of this function is the total number of vertices assigned nonzero values. The 2-rainbow independent domination number of G, , is the minimum weight of such a function. Motivated by a real-life application, we study the 2-rainbow independent domination number of the complementary prism of a graph G, which is constructed by taking G and its complement , and then adding edges between corresponding vertices. We provide tight bounds for , and characterize graphs for which the lower bound, i.e. , is attained. The obtained results can, in practice, enable the prediction of the cost estimate for a given communication or surveillance network.
Ključne besede: graph theory, domination, 2-rainbow independent domination, complementary prism
Objavljeno v DKUM: 23.04.2025; Ogledov: 0; Prenosov: 1
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4. STALITA: innovative platform for bank transactions analysisDavid Jesenko, Štefan Kohek, Borut Žalik, Matej Brumen, Domen Kavran, Niko Lukač, Andrej Živec, Aleksander Pur, 2022, izvirni znanstveni članek Opis: Acts of fraud have become much more prevalent in the financial industry with the rise
of technology and the continued economic growth in modern society. Fraudsters are evolving
their approaches continuously to exploit the vulnerabilities of the current prevention measures
in place, many of whom are targeting the financial sector. To overcome and investigate financial
frauds, this paper presents STALITA, which is an innovative platform for the analysis of bank
transactions. STALITA enables graph-based data analysis using a powerful Neo4j graph database
and the Cypher query language. Additionally, a diversity of other supporting tools, such as support
for heterogeneous data sources, force-based graph visualisation, pivot tables, and time charts, enable
in-depth investigation of the available data. In the Results section, we present the usability of the
platform through real-world case scenarios.
Ključne besede: Neo4j, platform, bank transactions, graph analysis, graph visualisation, fraud, investigation
Objavljeno v DKUM: 27.03.2025; Ogledov: 0; Prenosov: 3
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5. Knowledge graph alignment network with node-level strong fusionShuang Liu, Man Xu, Yufeng Qin, Niko Lukač, 2022, izvirni znanstveni članek Opis: Entity alignment refers to the process of discovering entities representing the same object
in different knowledge graphs (KG). Recently, some studies have learned other information about
entities, but they are aspect-level simple information associations, and thus only rough entity representations can be obtained, and the advantage of multi-faceted information is lost. In this paper, a
novel node-level information strong fusion framework (SFEA) is proposed, based on four aspects:
structure, attribute, relation and names. The attribute information and name information are learned
first, then structure information is learned based on these two aspects of information through graph
convolutional network (GCN), the alignment signals from attribute and name are already carried
at the beginning of the learning structure. In the process of continuous propagation of multi-hop
neighborhoods, the effect of strong fusion of structure, attribute and name information is achieved
and the more meticulous entity representations are obtained. Additionally, through the continuous
interaction between sub-alignment tasks, the effect of entity alignment is enhanced. An iterative
framework is designed to improve performance while reducing the impact on pre-aligned seed pairs.
Furthermore, extensive experiments demonstrate that the model improves the accuracy of entity
alignment and significantly outperforms 13 previous state-of-the-art methods.
Ključne besede: knowledge graph, entity ealignment, graph convolutional network, knowledge fusion
Objavljeno v DKUM: 27.03.2025; Ogledov: 0; Prenosov: 5
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6. Creating vector profile graph in ArcGIS Pro based on hiking trail tracking with AllTrails appKlemen Prah, 2024, izvirni znanstveni članek Opis: This paper proposes a model for creating a vector profile graph in ArcGIS Pro based on AllTrails tracking. The vector profile graph is important for route’s geometric measurements and spatial analysis in GIS. The model was created in an Excel table, based on the AllTrails output Excel data, and implemented in ArcGIS Pro. A model needed to be equipped with several attributes, including the coordinates of the initial and all other points of the vector profile graph. The same Excel model was also used to create a vector profile graph based on the output of the Stack Profile tool. The two vector profile graphs were compared with each other. Comparison showed significant differences in elevation and surface distance between them. In general, the profile graph created using the Stack Profile tool shows lower elevations and shorter surface distance. This study also points out the issues of positional error that can occur when tracking routes with smartphones, and the discrepancies in creating vector profile graphs using different approaches.
Ključne besede: vector profile graph, hiking route, distance, elevation, AllTrails
Objavljeno v DKUM: 26.03.2025; Ogledov: 0; Prenosov: 6
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7. Optimal L(d,1)-Labeling of Certain Direct Graph Bundles Cycles over Cycles and Cartesian Graph Bundles Cycles over CyclesIrena Hrastnik Ladinek, 2024, izvirni znanstveni članek Opis: An L(d,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least d and the labels on vertices at distance two differ by at least one, where d≥1. The span of f is the difference between the largest and the smallest numbers in f(V). The λ1d-number of G, denoted by λ1d(G), is the minimum span over all L(d,1)-labelings of G. We prove that λ1d(X)≤2d+2, with equality if 1≤d≤4, for direct graph bundle X=Cm×σℓCn and Cartesian graph bundle X=Cm□σℓCn, if certain conditions are imposed on the lengths of the cycles and on the cyclic ℓ-shift σℓ.
Ključne besede: L(d, 1)-labeling, λ d 1 -number, direct product of graph, direct graph bundle, Cartesian product of graph, Cartesian graph bundle, cyclic ℓ-shift, channel assignment
Objavljeno v DKUM: 13.03.2025; Ogledov: 0; Prenosov: 7
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8. A survey on packing coloringsBoštjan Brešar, Jasmina Ferme, Sandi Klavžar, Douglas F. Rall, 2020, pregledni znanstveni članek Opis: If S=(a1,a2,...) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1,X2,... such that for each pair of distinct vertices in the set Xi, the distance between them is larger than ai. If there exists an integer k such that V(G)=X1 U ... U Xk, then the partition is called an S-packing k-coloring. The S-packing chromatic number of G is the smallest k such that G admits an S-packing k-coloring. If ai=i for every i, then the terminology reduces to packing colorings and packing chromatic number. Since the introduction of these generalizations of the chromatic number in 2008 more than fifty papers followed. Here we survey the state of the art on the packing coloring, and ts generalization, the S-packing coloring. We also list several conjecres and open problems.
Ključne besede: packing coloring, packing chromatic number, subcubic graph, S-packing chromatic number, computational complexity
Objavljeno v DKUM: 11.03.2025; Ogledov: 0; Prenosov: 7
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9. Trees with distinguishing index equal distinguishing number plus oneSaeid Alikhani, Sandi Klavžar, Florian Lehner, Samaneh Soltani, 2020, izvirni znanstveni članek Opis: The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism. It is known that for every graph G we have D'(G) \leq D(G) + 1. In this note we characterize finite trees for which this inequality is sharp. We also show that if G is a connected unicyclic graph, then D'(G) = D(G).
Ključne besede: automorphism group, distinguishing index, distinguishing number, tree, unicyclic graph
Objavljeno v DKUM: 11.03.2025; Ogledov: 0; Prenosov: 4
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10. The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon moleculesMatevž Črepnjak, Martin Knor, Niko Tratnik, Petra Žigert Pleteršek, 2021, izvirni znanstveni članek Opis: The Graovac-Pisanski index, also called the modified Wiener index, was introduced in 1991 and represents an extension of the original Wiener index, because it considers beside the distances in a graph also its symmetries. Similarly as Wiener in 1947 showed the correlation of the Wiener indices of the alkane series with the boiling points, in 2018 the connection between the GraovacPisanski index and the melting points of some hydrocarbon molecules was established. In this paper, we prove that the Graovac-Pisanski index of any connected bipartite graph as well as of any connected graph on an even number of vertices is an integer number. These results are applied to some important families of hydrocarbon molecules. By using a computer programme, the graphs with a non-integer Graovac-Pisanski index on at most nine vertices are counted. Finally, an infinite class of unicyclic graphs with a non-integer Graovac-Pisanski index is described.
Ključne besede: modified Wiener index, Graovac-Pisanski index, graph distance, automorphism group, hydrocarbons, carbon nanostructures
Objavljeno v DKUM: 14.02.2025; Ogledov: 0; Prenosov: 4
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