1. Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problemsHauke Gravenkamp, Bor Plestenjak, Daniel A. Kiefer, Elias Jarlebring, 2025, izvirni znanstveni članek Povzetek: We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound in embedded plate structures or seismic waves in soil layers over an elastic half-space. We employ a semi-analytical formulation to describe the layers, thus discretizing the thickness direction by means of finite elements. For a free layer, this technique leads to a well-known quadratic eigenvalue problem for the mode shapes and corresponding horizontal wavenumbers. Incorporating the coupling conditions to account for the adjacent half-spaces gives rise to additional terms that are nonlinear in the wavenumber. We show that the resulting nonlinear eigenvalue problem can be cast in the form of a multiparameter eigenvalue problem whose solutions represent the wave numbers in the plate and in the half-spaces. The multiparameter eigenvalue problem is solved numerically using recently developed algorithms. Matlab implementations of the proposed methods are publicly available. Ključne besede: guided waves, plates, soil dynamics, half-space, leaky waves, semi-analytical method Objavljeno v DiRROS: 11.10.2024; Ogledov: 1; Prenosov: 2 Celotno besedilo (4,80 MB) Gradivo ima več datotek! Več... |
2. Symmetries of the Woolly Hat graphsLeah Berman, Sergio Hiroki Koike Quintanar, Elías Mochán, Alejandra Ramos Rivera, Primož Šparl, Steve Wilson, 2024, izvirni znanstveni članek Povzetek: A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length. While the tetravalent edge-transitive graphs admitting a semiregular automorphism with only one orbit are easy to determine, those that admit a semiregular automorphism with two orbits took a considerable effort and were finally classified in 2012. Of the several possible different "types" of potential tetravalent edge-transitive graphs admitting a semiregular automorphism with three orbits, only one "type" has thus far received no attention. In this paper we focus on this class of graphs, which we call the Woolly Hat graphs. We prove that there are in fact no edge-transitive Woolly Hat graphs and classify the vertex-transitive ones. Ključne besede: edge-transitive, vertex-transitive, tricirculant, Woolly Hat graphs Objavljeno v DiRROS: 07.10.2024; Ogledov: 58; Prenosov: 16 Celotno besedilo (555,34 KB) Gradivo ima več datotek! Več... |
3. On the 2-rainbow independent domination numbers of some graphsBoštjan Gabrovšek, Aljoša Peperko, Janez Žerovnik, 2023, izvirni znanstveni članek Povzetek: By suitably adjusting the tropical algebra technique we compute the rainbow independent domination numbers of several infinite families of graphs including Cartesian products $C_n \Box P_m$ and $C_n \Box C_m$ for all $n$ and $m\le 5$, and generalized Petersen graphs $P(n,2)$ for $n \ge 3$. Ključne besede: graph theory, rainbow independent domination number, path algebra, tropical algebra Objavljeno v DiRROS: 03.10.2024; Ogledov: 85; Prenosov: 37 Celotno besedilo (459,61 KB) Gradivo ima več datotek! Več... |
4. Inequalities and equalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operatorsKatarina Bogdanović, Aljoša Peperko, 2023, izvirni znanstveni članek Povzetek: We prove new inequalities and equalities for the generalized and the joint spectral radius (and their essential versions) of Hadamard (Schur) geometric means of bounded sets of positive kernel operators on Banach function spaces. In the case of nonnegative matrices that define operators on Banach sequences we obtain additional results. Our results extend results of several authors that appeared relatively recently. Ključne besede: Hadamard-Schur geometric mean, Hadamard-Schur product, joint and generalized spectral radius, essential spectral radius, measure of noncompactness, positive kernel operators, non-negative matrices, bounded sets of operators Objavljeno v DiRROS: 03.10.2024; Ogledov: 87; Prenosov: 61 Celotno besedilo (1,72 MB) Gradivo ima več datotek! Več... |
5. Covering the edges of a graph with trianglesCsilla Bujtás, Akbar Davoodi, Laihao Ding, Ervin Győri, Zsolt Tuza, Donglei Yang, 2025, izvirni znanstveni članek Povzetek: In a graph $G$, let $\rho_\triangle(G)$ denote the minimum size of a set of edges and triangles that cover all edges of $G$, and let $\alpha_1(G)$ be the maximum size of an edge set that contains at most one edge from each triangle. Motivated by a question of Erdős, Gallai, and Tuza, we study the relationship between $\rho_\triangle(G)$ and $\alpha_1(G)$ and establish a sharp upper bound on $\rho_\triangle(G)$. We also prove Nordhaus-Gaddum-type inequalities for the considered invariants. Ključne besede: edge-disjoint triangles, edge clique covering, Nordhaus-Gaddum inequality Objavljeno v DiRROS: 03.10.2024; Ogledov: 79; Prenosov: 43 Celotno besedilo (283,48 KB) Gradivo ima več datotek! Več... |
6. Vertex-primitive digraphs with large fixityMarco Barbieri, Primož Potočnik, 2024, izvirni znanstveni članek Povzetek: The relative fixity of a digraph $\Gamma$ is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of $\Gamma$ and the number of vertices of $\Gamma$ .We characterize the vertex-primitive digraphs whose relative fixity is at least $1 \over 3$, and we show that there are only finitely many vertex-primitive digraphs of bounded out-valency and relative fixity exceeding a positive constant. Ključne besede: vertex-primitive digraphs, fixity, product action, graphs Objavljeno v DiRROS: 03.10.2024; Ogledov: 88; Prenosov: 40 Celotno besedilo (397,05 KB) Gradivo ima več datotek! Več... |
7. Fast winning strategies for Staller in the Maker-Breaker domination gameCsilla Bujtás, Pakanun Dokyeesun, 2024, izvirni znanstveni članek Povzetek: The Maker-Breaker domination game is played on a graph $G$ by two players, called Dominator and Staller, who alternately choose a vertex that has not been played so far. Dominator wins the game if his moves form a dominating set. Staller wins if she plays all vertices from a closed neighborhood of a vertex $v \in V(G)$. Dominator's fast winning strategies were studied earlier. In this work, we concentrate on the cases when Staller has a winning strategy in the game. We introduce the invariant $\gamma'_{\rm SMB}(G)$ (resp., $\gamma_{\rm SMB}(G)$) which is the smallest integer $k$ such that, under any strategy of Dominator, Staller can win the game by playing at most $k$ vertices, if Staller (resp., Dominator) plays first on the graph $G$. We prove some basic properties of $\gamma_{\rm SMB}(G)$ and $\gamma'_{\rm SMB}(G)$ and study the parameters' changes under some operators as taking the disjoint union of graphs or deleting a cut vertex. We show that the inequality $\delta(G)+1 \le \gamma'_{\rm SMB}(G) \le \gamma_{\rm SMB}(G)$ always holds and that for every three integers $r,s,t$ with $2\le r\le s\le t$, there exists a graph $G$ such that $\delta(G)+1 = r$, $\gamma'_{\rm SMB}(G) = s$, and $\gamma_{\rm SMB}(G) = t$. We prove exact formulas for $\gamma'_{\rm SMB}(G)$ where $G$ is a path, or it is a tadpole graph which is obtained from the disjoint union of a cycle and a path by adding one edge between them. Ključne besede: domination game, Maker–Breaker game, winning number, Maker-Breaker domination game, closed neighborhood hypergraph Objavljeno v DiRROS: 03.10.2024; Ogledov: 88; Prenosov: 49 Celotno besedilo (503,82 KB) Gradivo ima več datotek! Več... |
8. A note on the 2-colored rectilinear crossing number of random point sets in the unit squareSergio Cabello, Éva Czabarka, Ruy Fabila-Monroy, Yuya Higashikawa, Raimund Seidel, László Székely, Josef Tkadlec, Alexandra Wesolek, 2024, izvirni znanstveni članek Povzetek: Let $S$ be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of $S$ with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the probability that $S$ defines a pair of crossing edges of the same color is equal to $1/4$. This is connected to a recent result of Aichholzer et al. who showed that by $2$-colouring the edges of a geometric graph and counting monochromatic crossings instead of crossings, the number of crossings can be more than halved. Our result shows that for the described random drawings, there is a coloring of the edges such that the number of monochromatic crossings is in expectation ${1 \over 2} - {7 \over 50}$ of the total number of crossings. Ključne besede: arrangement of points, flat, hyperplane Objavljeno v DiRROS: 03.10.2024; Ogledov: 81; Prenosov: 38 Celotno besedilo (504,15 KB) Gradivo ima več datotek! Več... |
9. Mutual-visibility in strong products of graphs via total mutual-visibilitySerafino Cicerone, Gabriele Di Stefano, Sandi Klavžar, Ismael G. Yero, 2024, izvirni znanstveni članek Povzetek: Let $G$ be a graph and $X\subseteq V(G)$. Then $X$ is a mutual-visibility set if each pair of vertices from $X$ is connected by a geodesic with no internal vertex in $X$. The mutual-visibility number $\mu(G)$ of $G$ is the cardinality of a largest mutual-visibility set. In this paper, the mutual-visibility number of strong product graphs is investigated. As a tool for this, total mutual-visibility sets are introduced. Along the way, basic properties of such sets are presented. The (total) mutual-visibility number of strong products is bounded from below in two ways, and determined exactly for strong grids of arbitrary dimension. Strong prisms are studied separately and a couple of tight bounds for their mutual-visibility number are given. Ključne besede: mutual-visibility set, mutual-visibility number, total mutual-visibility set, strong product of graphs Objavljeno v DiRROS: 02.10.2024; Ogledov: 106; Prenosov: 53 Celotno besedilo (618,95 KB) Gradivo ima več datotek! Več... |
10. |