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• Graph invariants are employed within the sciences of statistics, pattern recognition, computational geometry, biochemistry, and specifically chemicals to evaluate and construct data warehouses as well as chemical structures. • It is fascinating to see how numerous global features that have been established and developed within the paradigm of computational geometry present themselves in sophisticated connections. We examine the chemical graph of the crystal lattice of beryllium oxide (BeO) in this article. • Topological co-indices are crucial tools for investigations since they serve as molecular descriptors. Moreover, by connecting degree-based topological co-indices like, the first and second Zagreb co-indices, the atom bond connectivity co-index, the geometric arithmetic co-index, the forgotten co-index, the Balaban co-index, the augmented co-index, etc. • We can determine how much heat of formation was required to build these structures (BeO) by analysing the curve fitting methods for heat of formation. Graph invariants are employed within the sciences of statistics, pattern recognition, computational geometry, biochemistry, and specifically chemicals to evaluate and construct data warehouses as well as chemical structures. It is fascinating to see how numerous global features that have been established and developed within the paradigm of computational geometry present themselves in sophisticated connections. We examine the chemical graph of the crystal lattice of beryllium oxide (BeO) in this article. Topological co-indices are crucial tools for investigations since they serve as molecular descriptors. Moreover, by connecting degree-based topological co-indices like, the first and second Zagreb co-indices, the atom bond connectivity co-index, the geometric arithmetic co-index, the forgotten co-index, the Balaban co-index, the augmented co-index, etc. We can determine how much heat of formation was required to build these structures BeO by analysing the curve fitting methods for heat of formation. [ABSTRACT FROM AUTHOR]