1. A method for computing the edge-Hosoya polynomial with application to phenylenesMartin Knor, Niko Tratnik, 2023, izvirni znanstveni članek Opis: The edge-Hosoya polynomial of a graph is the edge version of the famous Hosoya polynomial. Therefore, the edge-Hosoya polynomial counts the number of (unordered) pairs of edges at distance $k \ge 0$ in a given graph. It is well known that this polynomial is closely related to the edge-Wiener index and the edge-hyper-Wiener index. As the main result of this paper, we greatly generalize an earlier result by providing a method for calculating the edge-Hosoya polynomial of a graph $G$ which is obtained by identifying two edges of connected bipartite graphs $G_1$ and $G_2$. To show how the main theorem can be used, we apply it to phenylene chains. In particular, we present the recurrence relations and a linear time algorithm for calculating the edge-Hosoya polynomial of any phenylene chain. As a consequence, closed formula for the edge-Hosoya polynomial of linear phenylene chains is derived. Ključne besede: edge-Hosoya polynomial, graphs, phenylenes Objavljeno v DKUM: 15.04.2024; Ogledov: 160; Prenosov: 178
Povezava na celotno besedilo Gradivo ima več datotek! Več... |
2. The multivariable Zhang-Zhang polynomial of phenylenesNiko Tratnik, 2023, izvirni znanstveni članek Opis: The Zhang-Zhang polynomial of a benzenoid system is a well-known counting polynomial that was introduced in 1996. It was designed to enumerate Clar covers, which are spanning subgraphs with only hexagons and edges as connected components. In 2018, the generalized Zhang-Zhang polynomial of two variables was defined such that it also takes into account 10-cycles of a benzenoid system. The aim of this paper is to introduce and study a new variation of the Zhang-Zhang polynomial for phenylenes, which are important molecular graphs composed of 6-membered and 4-membered rings. In our case, Clar covers can contain 4-cycles, 6-cycles, 8-cycles, and edges. Since this new polynomial has three variables, we call it the multivariable Zhang-Zhang (MZZ) polynomial. In the main part of the paper, some recursive formulas for calculating the MZZ polynomial from subgraphs of a given phenylene are developed and an algorithm for phenylene chains is deduced. Interestingly, computing the MZZ polynomial of a phenylene chain requires some techniques that are different to those used to calculate the (generalized) Zhang-Zhang polynomial of benzenoid chains. Finally, we prove a result that enables us to find the MZZ polynomial of a phenylene with branched hexagons. Ključne besede: Zhang-Zhang polynomial, phenylene, Clar cover, Kekulé structure Objavljeno v DKUM: 09.02.2024; Ogledov: 320; Prenosov: 22
Celotno besedilo (719,26 KB) Gradivo ima več datotek! Več... |
3. A new alternative to Szeged, Mostar, and PI polynomials : the SMP polynomialsMartin Knor, Niko Tratnik, 2023, izvirni znanstveni članek Opis: Szeged-like topological indices are well-studied distance-based molecular descriptors, which include, for example, the (edge-)Szeged index, the (edge-)Mostar index, and the (vertex-)PI index. For these indices, the corresponding polynomials were also defined, i.e., the (edge-)Szeged polynomial, the Mostar polynomial, the PI polynomial, etc. It is well known that, by evaluating the first derivative of such a polynomial at x = 1, we obtain the related topological index. The aim of this paper is to introduce and investigate a new graph polynomial of two variables, which is called the SMP polynomial, such that all three vertex versions of the above-mentioned indices can be easily calculated using this polynomial. Moreover, we also define the edge-SMP polynomial, which is the edge version of the SMP polynomial. Various properties of the new polynomials are studied on some basic families of graphs, extremal problems are considered, and several open problems are stated. Then, we focus on the Cartesian product, and we show how the (edge-)SMP polynomial of the Cartesian product of n graphs can be calculated using the (weighted) SMP polynomials of its factors. Ključne besede: SMP polynomial, edge-SMP polynomial, Cartesian product, Szeged index, Mostar index, PI index Objavljeno v DKUM: 09.02.2024; Ogledov: 262; Prenosov: 30
Celotno besedilo (320,27 KB) Gradivo ima več datotek! Več... |
4. Linearizability of 2:-3 resonant systems with quadratic nonlinearitiesMaja Žulj, Brigita Ferčec, Matej Mencinger, 2021, izvirni znanstveni članek Opis: In this paper, the linearizability of a 2:-3 resonant system with quadratic nonlinearities is studied. We provide a list of the conditions for this family of systems having a linearizable center. The conditions for linearizablity are obtained by computing the ideal generated by the linearizability quantities and its decomposition into associate primes. To successfully perform the calculations, we use an approach based on modular computations. The sufficiency of the obtained conditions is proven by several methods, mainly by the method of Darboux linearization. Ključne besede: polynomial systems, ODE's, linearizability problem, linearizability quantities, Darboux linearization, p:-q resonant system Objavljeno v DKUM: 01.08.2023; Ogledov: 576; Prenosov: 67
Celotno besedilo (434,06 KB) Gradivo ima več datotek! Več... |
5. Evolutionary-based prediction of ε50 for the lateral load-displacement behavior of piles in clayBabak Ebrahimian, Aida Nazari, 2013, izvirni znanstveni članek Opis: Analyzing piles that are subjected to lateral loads reveals that their behavior depends on the soil’s resistance at any point along the pile as a function of the pile’s deflection, known as the p-y curve. On the other hand, the deformation characteristics of soil defined as “the soil strain at 50% of maximum deviatoric stress (ε50)” have a considerable effect on the generated p-y curve. In this research, several models are proposed to predict ε50 specifically for designing the very long pile foundations of offshore oil and gas platforms in the South Pars field, Persian Gulf, Iran. Herein, ε50 is evaluated using extensive soil data, including in-situ and laboratory test results using evolutionary polynomial regression (EPR). The effects of the undrained shear strength, the normalized tip resistance of the cone penetration test, the over-burden pressure, the plasticity index and the over-consolidation ratio on ε50 are investigated in marine clays. It is demonstrated that the normalized cone tip resistance, which is an indication of the soil’s undrained shear strength, leads to more realistic ε50 values compared with the laboratory-derived undrained shear strength parameter. In addition, the application of the soil-index properties and the over-burden pressure in the models, improves their estimation quality. Furthermore, the results of full-scale lateral pile load tests at different sites are used in order to validate the performance of the proposed models when it comes to predicting the behavior of the lateral piles. Ključne besede: p-y curve, laterally loaded pile, piezocone penetration test, PCPT, marine clay, evolutionary polynomial regression, EPR, South Pars field Objavljeno v DKUM: 14.06.2018; Ogledov: 1095; Prenosov: 90
Celotno besedilo (676,68 KB) Gradivo ima več datotek! Več... |
6. Omega polynomial revisitedMircea V. Diudea, Sandi Klavžar, 2010, izvirni znanstveni članek Opis: Omega polynomial was proposed by Diudea (Omega Polynomial, Carpath. J. Math., 2006, 22, 43-47) to count the opposite topologically parallel edges in graphs, particularly to describe the polyhedral nanostructures. In this paper, the main definitions are re-analyzed and clear relations with other three related polynomials are established. These relations are supported by close formulas and appropriate examples. Ključne besede: mathematics, chemical graph theory, counting polynomials, Ommega polynomial, Theta polynomial, Pi polynomial, PI index, Sadhana polynomial, Cluj-Ilmenau index, CI index Objavljeno v DKUM: 24.08.2017; Ogledov: 1064; Prenosov: 120
Celotno besedilo (263,85 KB) Gradivo ima več datotek! Več... |
7. The Hosoya-Wiener polynomial of weighted treesBlaž Zmazek, Janez Žerovnik, 2007, izvirni znanstveni članek Opis: Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given. Ključne besede: mathematics, graph theory, Hosoya-Wiener polynomial, weighted tree, vertex weighted graphs Objavljeno v DKUM: 05.07.2017; Ogledov: 1394; Prenosov: 116
Celotno besedilo (182,69 KB) Gradivo ima več datotek! Več... |
8. Simplified computation of matchings in polygraphsAnte Graovac, Damir Vukičević, Damir Ježek, Janez Žerovnik, 2005, izvirni znanstveni članek Opis: Matching polynomial and perfect matchings for fasciagraphs, rotagraphs and twisted rotagraphs are treated in the paper. Classical transfer matrix approach makes it possible to get recursions for matching polynomial and perfect matchings, but the order of the matrix grows exponentially in the number of the linking edges between monographs. Novel transfer matrices are introduced whose order is much lower than that in classical transfer matrices. The virtue of the method introduced is especially pronounced when twoor more linking edges end in the same terminal vertex of a monograph. An example of a polyacene polygraph with extended pairings is given where a novel matrix has only 16 entries as compared to 65536 entries in the classical transfer matrix. However, all pairings are treated here on equal footing, but the method introduced can be applied to selected types of pairings of interest in chemistry. Ključne besede: polygraphs, matching polynomial, matchings, perfect matchings, Kekulé structures, extended structures, recursive enumeration, transfer matrix method Objavljeno v DKUM: 05.07.2017; Ogledov: 1583; Prenosov: 93
Celotno besedilo (102,97 KB) Gradivo ima več datotek! Več... |
9. On the codimension growth of simple color Lie superalgebrasDušan Pagon, Dušan Repovš, Mikhail Zaicev, 2012, izvirni znanstveni članek Opis: Predmet naših raziskav so polinomske identitete končno razsežnih enostavnih barvnih Liejevih superalgeber nad algebrsko zaprtim poljem z ničelno karakteristiko, gradacijo katerih podaja produkt dveh cikličnih grup reda 2. Dokazujemo, da kodimenzije opisanih identitet naraščajo eksponentno, stopnja te rasti pa je enaka razsežnosti dane algebre. Podoben rezultat smo dobili tudi za gradirane identitete in gradirane kodimenzije. Ključne besede: matematika, neasociativna algebra, Liejeve superalgebre, polinomske identitete, kodimenzije, eksponentna rast, mathematics, nonassociative algebra, color Lie superalgebras, polynomial identities, codimensions, exponential growth Objavljeno v DKUM: 10.07.2015; Ogledov: 1329; Prenosov: 31
Povezava na celotno besedilo |
10. Trace-positive polynomials and the quartic tracial moment problemSabine Burgdorf, Igor Klep, 2010, izvirni znanstveni članek Opis: V članku podamo nekomutativno različico klasičnega Hilbertovega izreka o pozitivnih polinomih stopnje 4 v 2 spremenljivkah: nekomutativni polinom takšnega tipa, ki ima pozitivno sled, je vsota štirih hermitskih kvadratov in komutatorjev. S pomočjo dualnosti ta rezultat uporabimo za študij problema momentov s sledjo. Ključne besede: matematika, nekomutativni polinom, sled, vsota hermitskih kvadratov, problem momentov, prosta pozitivnost, mathematics, noncommutative polynomial, trace, sum of hermitian squares, (truncated) moment problem, free positivity Objavljeno v DKUM: 10.07.2015; Ogledov: 1110; Prenosov: 111
Povezava na celotno besedilo |