Computation of Degree-Based Topological Descriptors Using M-Polynomial for Coronoid Systems

Julietraja, K.; Venugopal, P.

doi:10.1080/10406638.2020.1804415

Cited by 28 publications

(12 citation statements)

References 69 publications

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“…A coronoid system can be regarded as a benzenoid system that is allowed to have 'holes' such that the perimeter of the coronoid system and the perimeters of the holes are pairwise disjoint. There are many results on topological index of coronoid systems [33,34]. We now consider a special family of coronoid systems, denoted by K(n, p, r) (see Figure 6), which is formally generated from polycyclic benzenoid systems by circumcising some interior atoms or bonds.…”

Section: The Sombor Indices Of Graphene Coronoid Systems and Carbon Nanoconesmentioning

confidence: 99%

“…A coronoid system can be regarded as a benzenoid system that is allowed to have ‘holes’ such that the perimeter of the coronoid system and the perimeters of the holes are pairwise disjoint. There are many results on topological index of coronoid systems [33, 34]. We now consider a special family of coronoid systems, denoted by K ( n , p , r ) (see Figure 6), which is formally generated from polycyclic benzenoid systems by circumcising some interior atoms or bonds.Theorem Let G be the K ( n , p , r ) coronoid structure with r ≥ 1, n ≥ 3 and 1 ≤ p ≤ n. Then

\begin{matrix} centertrue \\ SO (G) = 4 \sqrt{13} (2 n + 4 p + 3 r - 6) + 3 \sqrt{2} [3 (3 r - 2) (2 p + n) + 9 r^{2} - 15 r + 16], \\ {italicSO}_{italicred} (G) = 4 \sqrt{5} (2 n + 4 p + 3 r - 6) + \sqrt{2} [4 (3 r - 2) (2 p + n) + 18 r^{2} - 30 r + 30], \\ {italicSO}_{italicavr} (G) = \frac{1}{r + 1} [4 \sqrt{r^{2} + 1} (2 n + 4 p + 3 r - 6) + \sqrt{2} (1 + 6 r)] . \end{matrix}

Proof .…”

Section: The Sombor Indices Of Graphene Coronoid Systems and Carbon Nanoconesmentioning

confidence: 99%

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The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

Fang

You

Liu

2021

Int J of Quantum Chemistry

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Hexagonal chains are a special class of catacondensed benzenoid system and phenylene chains are a class of polycyclic aromatic compounds. Recently, A family of Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these indices may be successfully applied on modeling thermodynamic properties of compounds. In this paper, we study the expected values of the Sombor indices in random hexagonal chains, phenylene chains, and consider the Sombor indices of some chemical graphs such as graphene, coronoid systems and carbon nanocones.

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Section: The Sombor Indices Of Graphene Coronoid Systems and Carbon Nanoconesmentioning

confidence: 99%

\begin{matrix} centertrue \\ SO (G) = 4 \sqrt{13} (2 n + 4 p + 3 r - 6) + 3 \sqrt{2} [3 (3 r - 2) (2 p + n) + 9 r^{2} - 15 r + 16], \\ {italicSO}_{italicred} (G) = 4 \sqrt{5} (2 n + 4 p + 3 r - 6) + \sqrt{2} [4 (3 r - 2) (2 p + n) + 18 r^{2} - 30 r + 30], \\ {italicSO}_{italicavr} (G) = \frac{1}{r + 1} [4 \sqrt{r^{2} + 1} (2 n + 4 p + 3 r - 6) + \sqrt{2} (1 + 6 r)] . \end{matrix}

Proof .…”

Section: The Sombor Indices Of Graphene Coronoid Systems and Carbon Nanoconesmentioning

confidence: 99%

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

Fang

You

Liu

2021

Int J of Quantum Chemistry

View full text Add to dashboard Cite

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“…ese special cases are used to predict the resonance energy of aromatic molecules and have attracted a great deal of interest in the field of theoretical chemistry as ideal models to explore conjugation circuits of π-electrons [34,35]. We will represent coronoid structure as…”

Section: Coronoid System C 1 [U V W X]mentioning

confidence: 99%

“…erefore, equation ( 1) with Tables 1 and 2 is in the form as follows: e coronoid system of D is delineated as C 2 [n, p, q, r], in which x ≥ 1, u ≥ 3, and 1 ≤ v < w ≤ u. Figure 3 shows the coronoid system of C 2 [u, v, w, x] [34,35].…”

Section: E Geometric Arithmetic Entropy C 1 [U V W X] Simple Calculations With Tablesmentioning

confidence: 99%

On Computation and Analysis of Topological Index‐Based Invariants for Complex Coronoid Systems

et al. 2021

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In chemical graph theory, benzenoid systems are interrogated as they exhibit the chemical compounds known as benzenoid hydrocarbons. Benzenoid schemes are circumscribed as planar connected finite graphs having no cut vertices wherein the entire internal sections are collaboratively congruent regular hexagon. The past couple of decennium has acknowledged an extravagant development regarding implementation of information theoretic framework in miscellaneous ramification of science, for instance, in social sciences, biological, physical, and engineering. Explicitly, this tremendous improvement has been outstanding in the field of soft computing, molecular biology, and information technology. The information theory, delineated by Claud Shannon, has no less importance when it was considered. Shannon put forwarded the apprehension of entropy to enumerate upper bounds in transmission rates in telephonic channels, in optical communication, and in wireless. The prestigious feature of entropy is that it entitles the amount of uncertainty in a system. The substantial participation of this paper is to explore characteristics of graph entropies and then keep moving forward to talk about the formation of coronoid polycyclic aromatic hydrocarbons. Likewise, we estimate entropies through precise topological indices established on degree of terminal nodes.

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“…The expressions for computing the values of nine VDB topological indices for r ‐circumscribed coronoid systems were obtained in Julietraja and Venugopal. [ 42 ]…”

Section: Introductionmentioning

confidence: 99%

Extremal values of vertex‐degree‐based topological indices of coronoid systems

Cruz

Santamaría-Galvis

Rada

2020

Int J of Quantum Chemistry

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A vertex‐degree‐based (VDB for short) topological index φ induced by the numbers {φi,j}, is defined for a graph G with n vertices as φ()G=∑1≤i≤j≤n−1mi,jφi,j, where mi,j is the number of edges in G joining vertices of degree i and j. Our main concern is to study VDB topological indices over important classes of coronoid systems. Recall that a coronoid system is a natural representation of a coronoid hydrocarbon and can be defined as a benzenoid‐like system with a hole. In this paper we determine the extremal values of a VDB topological index φ over the set of primitive coronoid systems, the set of catacondensed coronoid systems, and the set of circumscribed coronoid systems.

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Computation of Degree-Based Topological Descriptors Using M-Polynomial for Coronoid Systems

Cited by 28 publications

References 69 publications

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

On Computation and Analysis of Topological Index‐Based Invariants for Complex Coronoid Systems

Extremal values of vertex‐degree‐based topological indices of coronoid systems

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