By Ali Reza Ashrafi, Mircea V. Diudea
This contributed quantity is galvanized through the seminal discovery and id of C60. beginning with a accomplished dialogue that includes graphene dependent nanostructures, next chapters comprise topological descriptions of matrices, polynomials and indices, and a longer research of the symmetry and topology of nanostructures. Carbon allotropes similar to diamond and its connection to higher-dimensional areas is explored besides very important mathematical and topological issues. extra themes lined comprise spontaneous symmetry breaking in graphene, polyhedral carbon buildings, nanotube junction energetics, and cyclic polyines as family of nanotubes and fullerenes. This booklet is geared toward researchers lively within the examine of carbon fabrics technology and technology.
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Extra resources for Distance, Symmetry, and Topology in Carbon Nanomaterials
Will remain as an open question. V. Diudea and B. Szeﬂer Omega Polynomial in Polybenzenes Omega Polynomial in 3-Periodic Polybenzenes O’Keeffe et al. 82 D (also polybenzene, Fig. 5), is described to belong to the space group Pn3m and having the topology of the diamond. The second structure (Fig. 82 P and it belongs to the space group Im3m, corresponding to the P-type surface. In fact these networks represent embeddings of the hexagon patch in the two surfaces of negative curvature, D and P, respectively (Szeﬂer and Diudea 2012).
J Chem Inf Comput Sci 35:1011–1014 Harary F (1969) Graph theory. Addison-Wesley, Reading Imrich W, Klavžar S (1993) A simple O(mn) algorithm for recognizing Hamming graphs. Bull Inst Comb Appl 9:45–56 John PE, Khadikar PV, Singh J (2007a) A method of computing the PI index of benzenoid hydrocarbons using orthogonal cuts. J Math Chem 42:37–45 John PE, Vizitiu AE, Cigher S, Diudea MV (2007b) CI index in tubular nanostructures. MATCH Commun Math Comput Chem 57:479–484 Khadikar PV (2000) On a novel structural descriptor PI.
2 Omega Polynomial in 1-Periodic Polybenzenes The units BTA_48 (Fig. 5, left) and BTZ_24 (Fig. 7, left) can form “eclipsed” dimers that next provide hyper-pentagons (Fig. 7) and further multi-tori BTX20 (Fig. 8, left column) (Diudea and Szeﬂer 2012). Multi-tori are complex structures consisting of more than one single torus (Diudea and Nagy 2007; Diudea 2005; Diudea and Petitjean 2008). They can appear as self-assembly products of some repeating units/monomers (formed eventually by spanning of cages/fullerenes), as in spongy carbon or in natural zeolites.