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

Brezovnik, Simon; Tratnik, Niko

doi:10.46793/match.90-2.401b

Cited by 1 publication

(6 citation statements)

References 28 publications

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“…However, the cut method is not deduced only for SMP polynomials, but can be applied also for the introduced multivariable Szeged‐like polynomial, which encompasses numerous graph polynomials. Therefore, the result of this paper significantly improves the main contributions of papers [7,20]. More precisely, in [7] the cut method was developed for any Szeged‐like topological index, which means that it can not be used for graph polynomials.…”

Section: Discussionmentioning

confidence: 82%

“…In addition, if

ℰ = {E_{1}, …, E_{r}}

is any partition of

E (G)

, then we say that

ℰ

is coarser than

𝒰

if the set

E_{i}

is the union of one or more

Θ^{*}

‐classes of

G

for any

i \in {1, …, r}

. In such a case,

ℰ

is a c‐partition of the set

E (G)

[7,20].…”

Section: Preliminariesmentioning

confidence: 99%

“…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%

“…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%

“…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: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 82%

“…In addition, if

ℰ = {E_{1}, …, E_{r}}

is any partition of

E (G)

, then we say that

ℰ

is coarser than

𝒰

if the set

E_{i}

is the union of one or more

Θ^{*}

‐classes of

G

for any

i \in {1, …, r}

. In such a case,

ℰ

is a c‐partition of the set

E (G)

[7,20].…”

Section: Preliminariesmentioning

confidence: 99%

“…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%

“…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%

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

Self Cite

View full text Add to dashboard Cite

show abstract

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

Cited by 1 publication

References 28 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

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