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4. Semicubic cages and small graphs of even girth from voltage graphsFlor Aguilar, Gabriela Araujo-Pardo, Leah Berman, 2026, izvirni znanstveni članek Opis: A ({3, m}; g)-semicubic graph is a graph where the degree of each vertex is either 3 or m and the girth of the graph is g; if m = 3 we have a cubic graph. In this paper, we construct families of semicubic graphs of even girth and small order using two different techniques. The first technique generalizes a previous construction, which glues cubic cages of girth g together at remote vertices (vertices at distance at least g/2). The second technique, the main content of this paper, produces bipartite semicubic ({3, m}; g)-graphs of even girth g using voltage graphs over ℤm. For girth g = 4t + 2, t ≥ 1, the constructed graphs have two vertices of degree m. For girth g = 4t, t ≥ 2, the construction produces graphs with exactly three vertices of degree m (of course, the remaining vertices are of degree 3 in both cases). In particular, we describe infinite families of ({3, m}; g)−semicubic graphs for g = {6, 8, 10, 12} for infinitely many values of m. The cases g = {6, 8} include the unique 6-cage and the unique 8-cage when m = 3. The families obtained in this paper for girth g = {10, 12} include examples of orders that match the best-known bounds for ({3, m}; g)−semicubic graphs until this moment.
Ključne besede: Graph, semicubic graph, girth, voltage graph
Objavljeno v RUP: 17.08.2026; Ogledov: 9; Prenosov: 0
 Celotno besedilo (574,36 KB) |
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6. Centrality in connected graphs via convexity or concavityDinesh Pandey, Kamal Lochan Patra, 2026, izvirni znanstveni članek Opis: In graph theory, several central parts of graphs have been defined. The center, median and the security center are three such concepts defined for any connected graph, while others are specific to trees. These definitions typically involve a function defined on the vertex set of the graph.
This paper generalizes the concepts of convex and concave functions, originally defined for trees, to connected graphs. Using this, we provide a unified approach to prove the known results that each of the center, median, and security center of a connected graph is either a cut vertex or lies within a block. Additionally, we introduce three new central parts of a connected graph as generalizations of the subtree core, core vertices, and characteristic set of a tree, and examine their properties in relation to the center, median, and security center. We also show that for any graph G, there exists a supergraph G' such that the subgraph induced by the characteristic center of G' is isomorphic to G. Finally, we propose several open problems related to subgraph core and core center.
Ključne besede: Center, characteristic center, convex and concave functions, core center, median, security center, subgraph core
Objavljeno v RUP: 17.08.2026; Ogledov: 10; Prenosov: 1
Celotno besedilo (388,93 KB) |
7. 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: 10; Prenosov: 1
Celotno besedilo (511,43 KB) |
8. Mnenja slovenskih učiteljev tretjega vzgojno-izobraževalnega obdobja o uporabi razširjene resničnosti (XR) pri pouku : diplomsko deloAdnana Turkić, 2026, diplomsko delo Ključne besede: razširjena resničnost, obogatena resničnost, navidezna resničnost, mešana resničnost, izobraževanje, učitelji, tehnologija, osnovna šola
Objavljeno v RUP: 17.08.2026; Ogledov: 8; Prenosov: 1
Celotno besedilo (852,34 KB) |
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