Theoretical analysis reveals new upper bounds on graph energy using the Diaz-Metcalf inequality and topological indices, highlighting key structural constraints in network topology.
In this paper, we provide the upper bound on the energy of a graph using the Diaz-metcalf inequality. Then, we obtained several bounds on the energy of a graph with given invariants such as order, size, diameter, radius, girth, kirchoff index, clique number, algebraic connectivity, vertex connectivity, index, etc. Finally, we obtain several bounds on the energy of a graph in terms of many topological indices such as harmonic index, symmetric division degree index and modified second Zagreb indices.
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Khanra et al. (2026) studied this question.
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