Szeged and Mostar root-indices of graphs

Brezovnik, Simon; Dehmer, Matthias; Tratnik, Niko; Pleteršek, Petra Žigert

doi:10.1016/j.amc.2022.127736

Cited by 7 publications

(15 citation statements)

References 18 publications

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“…Moreover, the concepts of a general Szeged‐like topological index and a general Szeged‐like polynomial were introduced in [7] and [20], respectively: if

F

is a regular function for a strength‐weighted connected graph

G_{s w}

, then the Szeged‐like topological index of

G_{s w}

is defined as

T I_{F} (G_{s w}) = \sum_{e \in E (G)} w_{e} (e) F (e | G_{s w})

and the Szeged‐like polynomial of

G_{s w}

is defined as

S z P_{F} (G_{s w}; x) = \sum_{e \in E (G)} w_{e} (e) x^{F (e | G_{s w})} .

As an example, some Szeged‐like topological indices are defined in Table 1, where we assume

w_{v} \equiv 1

s_{e} \equiv 1

, and

s_{v} \equiv 0

.…”

Section: Multivariable Szeged‐like Polynomial Of Strength‐weighted Gr...mentioning

confidence: 99%

“…In particular, we introduce the multivariable Szeged-like polynomial, which includes SMP polynomials, and derive the cut method for computing this general polynomial of several variables. Note that the cut method is often used for simple computation of various distance-based topological indices [7,20,22,23].…”

Section: Moðgþ ¼ Xmentioning

confidence: 99%

“…Moreover, the concepts of a general Szeged-like topological index and a general Szeged-like polynomial were introduced in [7] and [20],…”

Section: Multivariable Szeged-like Polynomial Of Strength-weighted Gr...mentioning

confidence: 99%

“…The shared property of such polynomials is the fact that the first derivative of the polynomial at

x = 1

yields the corresponding topological index. Note that the concept of a general Szeged‐like polynomial was introduced in [20].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Cut method for the multivariable Szeged‐like polynomial with application to hyaluronic acid

Tratnik,

Žigert Pleteršek

2023

Int J of Quantum Chemistry

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Szeged‐like topological indices are commonly studied distance‐based molecular descriptors. These indices, together with related graph polynomials, offer valuable tools for characterising graph structures. Two new polynomials, the SMP polynomial and the edge‐SMP polynomial, have been recently introduced and allow efficient computation of Szeged, Mostar, and PI indices (note that the abbreviation SMP comes from the names of these indices). In this paper, we develop the cut method to compute different versions of the SMP polynomial in a much more general way. In particular, the multivariable Szeged‐like polynomial is introduced for any strength‐weighted graph. Moreover, it is shown how it can be computed using strength‐weighted quotient graphs obtained by a partition of the edge set coarser than the ‐partition. The developed approach is demonstrated by calculating weighted‐plus SMP polynomial and related topological indices for hyaluronic acid.

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“…Moreover, the concepts of a general Szeged‐like topological index and a general Szeged‐like polynomial were introduced in [7] and [20], respectively: if

F

is a regular function for a strength‐weighted connected graph

G_{s w}

, then the Szeged‐like topological index of

G_{s w}

is defined as

T I_{F} (G_{s w}) = \sum_{e \in E (G)} w_{e} (e) F (e | G_{s w})

and the Szeged‐like polynomial of

G_{s w}

is defined as

S z P_{F} (G_{s w}; x) = \sum_{e \in E (G)} w_{e} (e) x^{F (e | G_{s w})} .

As an example, some Szeged‐like topological indices are defined in Table 1, where we assume

w_{v} \equiv 1

s_{e} \equiv 1

, and

s_{v} \equiv 0

.…”

Section: Multivariable Szeged‐like Polynomial Of Strength‐weighted Gr...mentioning

confidence: 99%

Section: Moðgþ ¼ Xmentioning

confidence: 99%

“…Moreover, the concepts of a general Szeged-like topological index and a general Szeged-like polynomial were introduced in [7] and [20],…”

Section: Multivariable Szeged-like Polynomial Of Strength-weighted Gr...mentioning

confidence: 99%

“…The shared property of such polynomials is the fact that the first derivative of the polynomial at

x = 1

yields the corresponding topological index. Note that the concept of a general Szeged‐like polynomial was introduced in [20].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cut method for the multivariable Szeged‐like polynomial with application to hyaluronic acid

Tratnik,

Žigert Pleteršek

2023

Int J of Quantum Chemistry

Self Cite

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show abstract

“…It is worth mentioning that graph polynomials provide much more information about a graph than corresponding topological indices, since a polynomial is defined by several numbers (coefficients) which are themselves topological descriptors. Note also that Szeged-like polynomials were very recently used to introduce so-called root-indices of graphs, which have better discrimination power than the corresponding standard topological indices [14].…”

Section: Introductionmentioning

confidence: 99%

Generalized Cut Method for Computing Szeged–Like Polynomials with Applications to Polyphenyls and Carbon Nanocones

Brezovnik¹,

Tratnik²

2023

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Szeged, Padmakar-Ivan (PI), and Mostar indices are some of the most investigated distance-based Szeged-like topological indices. On the other hand, the polynomials related to these topological indices were also introduced, for example the Szeged polynomial, the edgeSzeged polynomial, the PI polynomial, the Mostar polynomial, etc. In this paper, we introduce a concept of the general Szeged-like polynomial for a connected strength-weighted graph. It turns out that this concept includes all the above mentioned polynomials and also infinitely many other graph polynomials. As the main result of the paper, we prove a cut method which enables us to efficiently calculate a Szeged-like polynomial by using the corresponding polynomials of strength-weighted quotient graphs obtained by a partition of the edge set that is coarser than Θ∗ -partition. To the best of our knowledge, this represents the first implementation of the famous cut method to graph polynomials. Finally, we show how the deduced cut method can be applied to calculate some Szeged-like polynomials and corresponding topological indices of para-polyphenyl chains and carbon nanocones.

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Topological descriptors, entropy measures and NMR spectral predictions for nanoporous graphenes with [14]annulene pores

Arockiaraj,

Raza,

Fiona

et al. 2023

Int J of Quantum Chemistry

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Porous two‐dimensional (2D) nanographene structures are materials with vast potentials in several areas of research with varied applications. The porous structures of these 2D‐materials offer multiple applications in the field of nanochemistry including sequestration of toxic metal ions as they possess large surface areas, enhanced electrical and electronic properties, and high mechanical flexibility. Their porous structures facilitate the creation of highly efficient electrodes, which could significantly improve the performance of batteries and other energy storage technologies. Topological descriptors are powerful tools for characterizing their structures and predicting the properties of molecules and thus have a number of applications. We compute the analytical expressions for degree‐based and Szeged‐type topological descriptors and their information‐theoretic entropies. In addition, we perform a comparative analysis of the scaled bond‐wise entropies between nanoporous graphenes and rectangular kekulene structures with comparable sizes. Furthermore, we predict the C and proton NMR spectral patterns of these materials using graph‐theoretical techniques.

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Szeged and Mostar root-indices of graphs

Cited by 7 publications

References 18 publications

Cut method for the multivariable Szeged‐like polynomial with application to hyaluronic acid

Cut method for the multivariable Szeged‐like polynomial with application to hyaluronic acid

Generalized Cut Method for Computing Szeged–Like Polynomials with Applications to Polyphenyls and Carbon Nanocones

Topological descriptors, entropy measures and NMR spectral predictions for nanoporous graphenes with [14]annulene pores

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