Abstract
Graph theory has provided chemist with a variety of useful tools, such as topological indices. A topological index Top(G) of a graph G is a number with the property that for every graph H isomorphic to G, Top(H) = Top(G). In this article, we present exact expressions for some topological indices of carbon compound graphene. We compute first Zagreb index, second Zagreb index, first multiple Zagreb index, second multiple Zagreb index, augmented Zagreb index, harmonic index and hyper-Zagreb index of graphene. These are some topological indices based on degrees.
Highlights
Graphene is an atomic-scale honeycomb lattice made of carbon atoms
A graph invariant is any function on a graph that does not depend on a labelling of its vertices
By IUPAC terminology, a topological index is a numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity
Summary
Graphene is an atomic-scale honeycomb lattice made of carbon atoms It is one of the most promising nanomaterials because of its unique combination of excellent properties, which opens a way for its exploitation in a wide spectrum of applications ranging from electronics to optics, sensors and biodevices. It is the most effective material for electromagnetic interference shielding. A molecular graph is a representation of the structural formula of a chemical compound in terms of graph theory, whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. We determine the topological indices such as Zagreb indices, multiple Zagreb indices, augmented Zagreb index, harmonic index and hyper-Zagreb index of graphene
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