Distance, Symmetry, and Topology in Carbon Nanomaterials

Distance, Symmetry, and Topology in Carbon Nanomaterials


Author:
Ali Reza Ashrafi & Mircea V. Diudea
Published in:
Springer
Release Year: 2016
ISBN: 978-3-319-31584-3
Pages: 481
Edition: Volume 9
File Size: 12 MB
File Type: pdf
Language: English



Description Distance, Symmetry, and Topology in Carbon Nanomaterials


In 1872, Felix Klein published his pioneering paper on the importance of symmetry, which was later named “Erlanger Programm” for his professorship at the University of Erlangen, Germany. He wrote: “we can say that geometry studies those and only those properties of the figure F which are shared by F and all the figures which are equal to F”. He continued that the most essential idea required in the study of symmetry is that of a group of space transformations. Topology is the mathematical study of shapes. Distance, Symmetry, and Topology in Carbon Nanomaterials gather the contributions of some leading experts in a new branch of science that is recently named “Mathematical Nanoscience”.
This volume continues and expands upon the previously published titles The Mathematics and Topology of Fullerenes (Carbon Materials: Chemistry and Physics series, Vol. 4, Springer 2011) and Topological Modelling of Nanostructures and Extended Systems(Carbon Materials: Chemistry and Physics series, Vol. 7, Springer 2013) by presenting the latest research on this topic. It introduces a new attractive field of research like the symmetry-based topological indices, multi-shell clusters, dodecahedron nano-assemblies, and generalized fullerenes, which allow the reader to obtain a better understanding of the physicochemical properties of nanomaterials.
Topology and symmetry of nanomaterials like fullerenes, generalized fullerenes, multi-shell clusters, graphene derivatives, carbon nanocones, course lattices, diamonds, dendrimers, tetrahedral nanoclusters, and cyclic carbon polyynes give some important information about the geometry of these new materials that can be used for correlating some of their physicochemical or biological properties. We would like to thank to all the authors for their work and support, also to Springer for giving us the opportunity to publish this edited book and finally to Springer people who allowed all our efforts to make this an interesting book.

Content of Distance, Symmetry, and Topology in Carbon Nanomaterials



1 Molecular Dynamics Simulation of Carbon Nanostructures:
The Nanotubes ........................................ 1
Istva ́n La ́szlo and Ibolya Zsoldos
2 Omega Polynomial in Nanostructures . . . . . . . . . . . . . . . . . . . . . . . 13
Mircea V. Diudea and Beata Szefler
3 An Algebraic Modification of Wiener and Hyper–Wiener Indices
and Their Calculations for Fullerenes . . . . . . . . . . . . . . . . . . . . . . . 33
Fatemeh Koorepazan-Moftakhar, Ali Reza Ashrafi,
Ottorino Ori, and Mihai V. Putz
4 Distance Under Symmetry: (3,6)-Fullerenes . . . . . . . . . . . . . . . . . . 51
Ali Reza Ashrafi, Fatemeh Koorepazan  Moftakhar, and Mircea V.
Diudea
5 Topological Symmetry of Multi-shell Clusters . . . . . . . . . . . . . . . . 61
Mircea V. Diudea, Atena Parvan-Moldovan, Fatemeh
Koorepazan-Moftakhar, and Ali Reza Ashrafi
6 Further Results on Two Families of Nanostructures . . . . . . . . . . . . 83
Zahra Yarahmadi and Mircea V. Diudea
7 Augmented Eccentric Connectivity Index of Grid Graphs . . . . . . . 95
Tomislav Dosˇlic ́ and Mojgan Mogharrab
8 Cluj Polynomial in Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . 103
Mircea V. Diudea and Mahboubeh Saheli
9 Graphene Derivatives: Carbon Nanocones and CorSu Lattice:
A Topological Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Farzaneh Gholaminezhad and Mircea V. Diudea

10 Hosoya Index of Splices, Bridges, and Necklaces . . . . . . . . . . . . . . 147
Tomislav Dosˇlic ́ and Reza Sharafdini
11 The Spectral Moments of a Fullerene Graph and Their
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
G.H. Fath-Tabar, F. Taghvaee, M. Javarsineh, and A. Graovac
12 Geometrical and Topological Dimensions of the Diamond . . . . . . . 167
G.V. Zhizhin, Z. Khalaj, and M.V. Diudea
13 Mathematical Aspects of Omega Polynomial . . . . . . . . . . . . . . . . . 189
Modjtaba Ghorbani and Mircea V. Diudea
14 Edge-Wiener Indices of Composite Graphs . . . . . . . . . . . . . . . . . . 217
Mahdieh Azari and Ali Iranmanesh
15 Study of the Bipartite Edge Frustration of Graphs . . . . . . . . . . . . . 249
Zahra Yarahmadi
16 The Hosoya Index and the Merrifield–Simmons Index of Some
Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Asma Hamzeh, Ali Iranmanesh, Samaneh Hossein–Zadeh,
and Mohammad Ali Hosseinzadeh
17 Topological Indices of 3-Generalized Fullerenes . . . . . . . . . . . . . . . 281
Z. Mehranian and A.R. Ashrafi
18 Study of the Matching Interdiction Problem in Some Molecular
Graphs of Dendrimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
G.H. Shirdel and N. Kahkeshani
19 Nullity of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Modjtaba Ghorbani and Mahin Songhori
20 Bondonic Chemistry: Spontaneous Symmetry Breaking
of the Topo-reactivity on Graphene . . . . . . . . . . . . . . . . . . . . . . . . 345
Mihai V. Putz, Ottorino Ori, Mircea V. Diudea, Beata Szefler,
and Raluca Pop
21 Counting Distance and Szeged (on Distance) Polynomials
in Dodecahedron Nano-assemblies . . . . . . . . . . . . . . . . . . . . . . . . . 391
Sorana D. Bolboaca ̆ and Lorentz Ja ̈ntschi
22 Tetrahedral Nanoclusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
Csaba L. Nagy, Katalin Nagy, and Mircea V. Diudea
23 Cyclic Carbon Polyynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
Lorentz Ja ̈ntschi, Sorana D. Bolboaca ̆, and Dusanka Janezic

24 Tiling Fullerene Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
Ali Asghar Rezaei
25 Enhancing Gauge Symmetries Via the Symplectic Embedding
Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
Salman Abarghouei Nejad and Majid Monemzadeh
26 A Lower Bound for Graph Energy of Fullerenes . . . . . . . . . . . . . . 463
Morteza Faghani, Gyula Y. Katona, Ali Reza Ashrafi,
and Fatemeh Koorepazan-Moftakhar
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
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