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The M-polynomials and topological indices of toroidal polyhex network

Muhammad Ajmal, Waqas Nazeer, Mobeen Munir, Shin Min Kang, Chahn Yong Jung
2017 International Journal of Mathematical Analysis  
A topological index of graph G is 1,2 Corresponding authors 306 Muhammad Ajmal et al. a numerical parameter related to G which characterizes its molecular topology.  ...  The M -polynomial of different molecular structures helps us to calculate many topological indices.  ...  The concept of degree is somewhat closely related to the concept of valence in chemistry. For details on bases of graph theory, any standard text such as [29] can be of great help.  ... 
doi:10.12988/ijma.2017.7119 fatcat:hue73rxh45eezhvqf63ivcxg24

Some Algebraic Polynomials and Topological Indices of Generalized Prism and Toroidal Polyhex Networks

Muhammad Ajmal, Waqas Nazeer, Mobeen Munir, Shin Kang, Young Kwun
2016 Symmetry  
A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs.  ...  In this report, we compute closed forms of first Zagreb, second Zagreb, and forgotten polynomials of generalized prism and toroidal polyhex networks.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym9010005 fatcat:dmovi5ekejdglkrgi3tofaaqge

Face-width of Pfaffian Braces and Polyhex Graphs on Surfaces [article]

Dong Ye, Heping Zhang
2013 arXiv   pre-print
The number of perfect matchings of Pfaffian graphs can be computed in polynomial time. In this paper, by applying the characterization of Pfaffian braces due to Robertson, Seymour and Thomas [Ann.  ...  Combining with polyhex graphs with face-width 2, we show that a bipartite polyhex graph is Pfaffian if and only if it is isomorphic to the cube, the Heawood graph or C_k× K_2 for even integers k> 6, and  ...  Polyhex graphs are also considered as an extension of fullerene graphs on other surfaces [3] , which have extensively applications in chemistry and material science [9, 10] .  ... 
arXiv:0908.1506v2 fatcat:lcz7347qnra45bhgu5wwjq6f4e

k-resonance in Toroidal Polyhexes*

Wai Chee Shiu, Peter Che Bor Lam, Heping Zhang
2005 Journal of Mathematical Chemistry  
Characterizations for 1, 2 and 3-resonant toroidal polyhexes are given respectively in this paper.  ...  This paper considers the k-resonance of a toroidal polyhex (or toroidal graphitoid) with a string (p, q, t) of three integers (p ≥ 2, q ≥ 2, 0 ≤ t ≤ p − 1).  ...  There have been a few work in the enumeration of perfect matchings of toroidal polyhexes by applying various techniques, such as transfer-matrix [12, 21] , permanent of the adjacency matrix [1] , and  ... 
doi:10.1007/s10910-004-6897-4 fatcat:ous4cp4i35hbflig3tkebqryxa

On some counting polynomials in chemistry

Haruo Hosoya
1988 Discrete Applied Mathematics  
Note that for such kj with no proper sextet, such as k, in Fig. 12 Now try to apply the sextet rotation to the set of the Kekult patterns for the graph in Fig. 12 .  ...  In chemistry we often need to know the electronic structure of a molecule so as to interpret the ultraviolet and visible absorption spectra of the molecule, to understand the reactivity and various related  ... 
doi:10.1016/0166-218x(88)90017-0 fatcat:gkh7ezvkbzh4harc6bnkkpkacm

Allowed Boundary Sequences for Fused Polycyclic Patches and Related Algorithmic Problems

Michel Deza, Patrick W. Fowler, Viatcheslav Grishukhin
2001 Journal of chemical information and computer sciences  
Hexagonal and pentagonal sequences of length at most 8 are tabulated, the former corresponding to planar benzenoid hydrocarbons C x H y with y up to 14.  ...  We consider sequences that encode boundary circuits of fused polycycles made up of polygonal faces with p sides, p e 6.  ...  ACKNOWLEDGMENT We thank the University of Exeter Research Committee and the European Union Framework IV program (TMR Network Contract FMRX CT97 0192 BIOFULLERENES) for financial support of this research  ... 
doi:10.1021/ci000060o pmid:11277715 fatcat:xgd2clcfpzdajkyrunn3emv3oq

A computer-based method to determine predictive potential of distance-spectral descriptors for measuring the π-electronic energy of benzenoid hydrocarbons with applications

S. Hayat, S. Khan, A. Khan, M. Imran
2021 IEEE Access  
INDEX TERMS Graph signal processing, quantum chemistry, chemical graph theory, eigenvalues-based topological descriptors, π-electronic energy, Benzenoid hydrocarbons, carbon nanotubes, carbon nanocones  ...  Applications of our computational method to certain infinite families of carbon nanotubes and carbon nanocones are presented.  ...  ACKNOWLEDGMENT The authors would like to thank their sincere gratitude to the reviewers for their helpful comments which have played a vital role in improving the quality and presentation of the original  ... 
doi:10.1109/access.2021.3053270 fatcat:cglmtmjw4jalrpt54ahfw67b3i


Sandi Klavžar, Sergey Shpectorov
2009 European journal of combinatorics (Print)  
Then they apply this concept to the convexity spaces coming from bipartite graphs.  ...  In organic chemistry, where the structure of a molecule can be represented by a connected graph, this point of view led to the development of a number of numerical invariants (or indices) which correlate  ... 
doi:10.1016/j.ejc.2008.09.013 fatcat:5mv54y53afeono2cw24yd2lzay


J. Xu, M.K. Siddiqui, M.R. Farahani, I.N. Cangul
2020 International Journal of Applied Mathematics  
A topological index is a numerical parameter of a graph which characterizes some of the topological properties of the graph.  ...  The concepts of hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index and relatedly the Zagreb polynomials were established in chemical graph theory by means of the vertex degrees  ...  of the Excellent Young Talents Support of Higher Education in Anhui Province (gxyq2018116); the Natural Science Foundation of Bozhou University (BYZ2018B03).  ... 
doi:10.12732/ijam.v32i6.1 fatcat:fvdeyopx3jdqxiq4jib7zoufn4

Graph theoretical invariants and elementary subgraphs of polyhex and polypent/polyhex systems of chemical relevance

Jerry Ray Dias
1996 Discrete Applied Mathematics  
algorithms that are highly useful for understanding and studying the structural properties of the classes of molecules that are isomorphic to the polyhex and polypent/polyhex graphs.  ...  + n = 2, a myriad of invariants have evolved for describing the properties of molecular graphs (graphs representing molecules).  ...  The a-bond skeleton of a benzenoid (PAH6) is isomorphic to a polyhex, and herein polyhex graphs will be used to represent molecular graphs of benzenoids [8] .  ... 
doi:10.1016/0166-218x(95)00012-g fatcat:k7bknejbdjffrcl55vcj3kbv3q

Page 4661 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
Summary: “An expanded form of the Wiener number is suggested for characterization of molecular graphs and structure-property correlations.  ...  The authors attempt to place these formal models in the more general theoretical context of sociological action theory as devel- oped by T.  ... 

Page 5244 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
Summary: “The correspondence between a graph and a geneal- ogy is used to apply techniques from the field of graph theory to genetic epidemiology.  ...  The theorems proved for these structures are applied to introduce an axiomatic characterization for Choquet expected utility and Quiggin’s anticipated utility.  ... 

On Computation of Face Index of Certain Nanotubes

Ansheng Ye, Aisha Javed, Muhammad Kamran Jamil, Kanza Abdul Sattar, Adnan Aslam, Zahid Iqbal, Asfand Fahad
2020 Discrete Dynamics in Nature and Society  
Topological index is a number that can be used to characterize the graph of a molecule. Topological indices describe the physical, chemical, and biological properties of a chemical structure.  ...  In this paper, we derive the analytical closed formulas of face index of some planar molecular structures such as TUC4, TUC4C8S, TUHC6, TUC4C8R, and armchair TUVC6.  ...  A topological index (TI) is an invariant that is assigned to a molecular structure (graph) and is used to characterize the molecule.  ... 
doi:10.1155/2020/3468426 fatcat:hq7wxqrxbfcndhd4aqzevuouy4

Page 2973 of Mathematical Reviews Vol. , Issue 81H [page]

1981 Mathematical Reviews  
They also utilize the spectrum of a graph, and a polyhex representation of a geographic region as models.  ...  Cliff, Haggett and Ord properly view Euler’s negative solution of the K6nigsberg~bridge problem as the historically first appli- cation of graph theory to geography.  ... 

Multiplicative Reverse Geometric-Arithmetic Indices and Arithmetic-Geometric of Silicate Network

2021 Biointerface Research in Applied Chemistry  
In mathematical chemistry, geometric-arithmetic and arithmetic-geometric indices are helpful from both theoretical and practical points of view.  ...  Acknowledgments The author would like to thank Dr.B.J.Gireesha, Department of mathematics, Kuvempu University, who motivated and inspired me to research. Further, I would like to thank Dr. N.  ...  Narahari, Department of mathematics, Tumkur university, for many useful suggestions.  ... 
doi:10.33263/briac123.41924199 fatcat:apoj6fxuc5g47bnl4upjadwba4
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