Abstract
Let G be a graph on n vertices. The Estrada index and Energy of G are invariants that are calculated from the eigenvalues of the adjacency matrix of a graph. The Estrada index, from the point of view of connectivity, is an interesting invariant to investigate as it allows the study and detection of the 3D properties of molecules and thus be able to compare them. A graphene sheet is an atomic-scale honeycomb lattice composed of carbon atoms linked in hexagonal shapes, with each carbon atom covalently bonded to three other carbon atoms. In this paper, considering the spectral theory of graphs as a tool, we study a way to discretize the graphene sheet and establish lower bounds for the Estrada index of this chemistry structure.
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