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A new alternative to Szeged, Mostar, and PI polynomials : the SMP polynomials
Martin 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: 197; Prenosov: 15
.pdf Celotno besedilo (320,27 KB)
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Szeged and Mostar root-indices of graphs
Simon Brezovnik, Matthias Dehmer, Niko Tratnik, Petra Žigert Pleteršek, 2023, izvirni znanstveni članek

Opis: Various distance-based root-indices of graphs are introduced and studied in the present article. They are obtained as unique positive roots of modified graph polynomials. In particular, we consider the Szeged polynomial, the weighted-product Szeged polynomial, the weighted-plus Szeged polynomial, and the Mostar polynomial. We derive closed formulas of these polynomials for some basic families of graphs. Consequently, we provide closed formulas for some root-indices and examine the convergence of sequences of certain root-indices. Moreover, some general properties of studied root-indices are stated. Finally, numerical results related to discrimination power, correlations, structure sensitivity, and abruptness of root-indices are calculated, interpreted, and compared to already known similar descriptors.
Ključne besede: Szeged index, Szeged polynomial, Mostar polynomial, root-index, discrimination power, sensitivity
Objavljeno v DKUM: 18.08.2023; Ogledov: 390; Prenosov: 44
.pdf Celotno besedilo (535,31 KB)
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Szeged-like topological indices and the efficacy of the cut method: the case of melem structures
Micheal Arockiaraj, Shagufa Mushtaq, Sandi Klavžar, J. Celin Fiona, Krishnan Balasubramanian, 2022, izvirni znanstveni članek

Opis: The Szeged index is a bond-additive topological descriptor that quantifies each bond's terminal atoms based on their closeness sets which is measured by multiplying the number of atoms in the closeness sets. Based on the high correlation between the Szeged index and the physico-chemical properties of chemical compounds, Szeged-like indices have been proposed by considering closeness sets with bond counts and other mathematical operations like addition and subtraction. As there are many ways to compute the Szeged-like indices, the cut method is predominantly used due to its complexity compared to other approaches based on algorithms and interpolations. Yet, we here analyze the usefulness of the cut method in the case of melem structures and find that it is less effective when the size and shape of the cavities change in the structures.
Ključne besede: distance, Szeged index, cut-method
Objavljeno v DKUM: 11.08.2023; Ogledov: 343; Prenosov: 32
.pdf Celotno besedilo (551,00 KB)
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Computing the Szeged index
Janez Žerovnik, 1996, izvirni znanstveni članek

Opis: We give an explicit algorithm for computing the Szeged index of a graph which runs in ▫$O(mn)$▫ time, where ▫$n$▫ is the number of nodes and ▫$m$▫ is the number of edges.
Ključne besede: mathematics, chemistry, chemical graph theory, molecular graphs, structural formulae, algorithms, topological index, Szeged index
Objavljeno v DKUM: 05.07.2017; Ogledov: 1725; Prenosov: 114
.pdf Celotno besedilo (1,83 MB)
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