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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 {x_{1}, x_{2}, …, x_{n}} of real numbers. A permutation f: X → X is a symmetry of X if d (f (x_{i}), f (x_{j})) = d (x_{i},x_{j}), 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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