Iskanje po katalogu digitalne knjižnice

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
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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
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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
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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
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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
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