Symmetry and Topology of Graphenes

Authored by: A. R. Ashrafi , F. Koorepazan-Moftakhar , O. Ori

Graphene Science Handbook

Print publication date:  April  2016
Online publication date:  April  2016

Print ISBN: 9781466591370
eBook ISBN: 9781466591387
Adobe ISBN:

10.1201/b19461-12

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Abstract

Graphene is an allotrope of carbon. These are two-dimensional materials consisting of a single layer of carbon atoms arranged in a regular hexagonal pattern similar to graphite. The mathematics of these objects constitutes a significant part of mathematical physics. Suppose X is a physical object that can be described by a finite set {x1, x2, …, xn} of real numbers. A permutation f: X → X is a symmetry of X if d (f (xi), f (xj)) = d (xi,xj), where d (−,−) is a given distance function. In this chapter, we first study the symmetry structure of some classes of graphene lattice and then apply this information to compute distance-based topological indices of some classes of graphenes.

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