Some Invariants of Jahangir Graphs

Munir, Mobeen; Nazeer, Waqas; Kang, Shin Min; Qureshi, Muhammad Imran; Nizami, Abdul Rauf; Kwun, Youl Chel

doi:10.3390/sym9010017

Cited by 17 publications

(13 citation statements)

References 23 publications

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“…M-polynomial got advantage over this approach as we only need to operate speci c di erential, integral or both operators on corresponding polynomial to get various vertex-based indices. Many closed form degree-based topological indices of Triangular Boron Nanotubes and Jahangir graph Jn,m are computed using M-polynomial [34,35]. The Zhang-Zhang polynomial (Clar covering polynomial), were found to occur for computation of the total π-electron energy of the molecules within speci c approximate expressions.…”

Section: Applications Of Topological Polynomialsmentioning

confidence: 99%

Molecular Properties of Symmetrical Networks Using Topological Polynomials

et al. 2019

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A numeric quantity that comprehend characteristics of molecular graph Γ of chemical compound is known as topological index. This number is, in fact, invariant with respect to symmetry properties of molecular graph Γ. Many researchers have established, after diverse studies, a parallel between the physico chemical properties like boiling point, stability, similarity, chirality and melting point of chemical species and corresponding chemical graph. These descriptors defined on chemical graphs are extremely helpful for researchers to conduct regression model like QSAR/QSPR and better understand the physical features, complexity of molecules, chemical and biological properties of underlying compound.In this paper, several structure descriptors of vital importance, namely, first, second, modified and augmented Zagreb indices, inverse and general Randic indices, symmetric division, harmonic, inverse sum and forgotten indices of Hex-derived Meshes (networks) of two kinds, namely, HDN1(n) and HDN2(n) are computed and recovered using general approach of topological polynomials.

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Section: Applications Of Topological Polynomialsmentioning

confidence: 99%

Molecular Properties of Symmetrical Networks Using Topological Polynomials

et al. 2019

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“…In Bashir et al [2], defined dendrimers by three components: a central core, an interior dendritic structure (the branches), and an exterior surface to compute the first and second Zagreb indices for poly(propyl) ether imine, porphyrin dendrimers and zinc‐porphyrin dendrimers. The authors computed first and second Zagreb indices, hyper Zagreb index, Symmetric division index and modified Zagreb index for Jahangir graphs in Munir et al [3], also the authors find the M ‐polynomial for the Jahangir graphs. The authors described their results by presenting the graphical analysis.…”

Section: Introductionmentioning

confidence: 99%

Face index of nanotubes and regular hexagonal lattices

Ding

Qureshi

Shah

et al. 2021

Int J of Quantum Chemistry

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The interdependency of the molecular structures of drugs and their biomedical characteristics have already been proved by lab experiments. We can approximate these characteristics by computing numerical invariants associated to their molecular structures. These invariants are called topological indices. Among many topological indices, the face index (FI) is defined most recently. The FI may be helpful in approximating the boiling point and π‐electron energy of benzenoid hydrocarbons and some other drugs with the correlation coefficient r>.99. In this article, we compute the FI for Boron triangular nanotubes, the nanotubes VC5V7[]p,q and HC5C7[]p,q, Also compute the FI for quadrilateral sections cut from regular hexagonal lattice Pmn and Pm+1/2n.

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“…In 2015, Deutsch and Klavžar gave M-polynomial, first Zagreb, and second Zagreb indices of polyomino chains, starlike trees, and triangulenes [2]. In 2017, Mobeen gave M-polynomial and several degree-based topological indices of titania nanotubes [10], of triangular boron nanotubes [11], and of Jahangir graph [12]. In 2017, Ajmal gave M-polynomial and topological indices of generalized prism network [13].…”

Section: Introductionmentioning

confidence: 99%

“…e augmented Zagreb index was proposed by Furtula in 2010 in [26] and is useful for computing heat of information of alkanes [18,27]. To know more about topological indices, their computing, and their applications, we refer the reader to [2,8,11,12,[28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Polynomials and General Degree‐Based Topological Indices of Generalized Sierpinski Networks

Fan¹,

Munir

Hussain

et al. 2021

Complexity

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Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems. In this article, we compute various connectivity polynomials such as M -polynomial, Zagreb polynomials, and forgotten polynomial of generalized Sierpinski networks S k n and recover some well-known degree-based topological indices from these. We also compute the most general Zagreb index known as α , β -Zagreb index and several other general indices of similar nature for this network. Our results are the natural generalizations of already available results for particular classes of such type of networks.

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Some Invariants of Jahangir Graphs

Cited by 17 publications

References 23 publications

Molecular Properties of Symmetrical Networks Using Topological Polynomials

Molecular Properties of Symmetrical Networks Using Topological Polynomials

Face index of nanotubes and regular hexagonal lattices

Polynomials and General Degree‐Based Topological Indices of Generalized Sierpinski Networks

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