Abstract
A useful extension of the Laplacian matrix is proposed here and the corresponding modification of the Laplacian energy (LE) is presented. The neighbourhood degree sum-based Laplacian energy (LNE) is produced by means of the eigenvalues of the newly introduced neighbourhood degree sum-based Laplacian matrix (LN). We investigate the mathematical properties of LNE by comparing it with the Laplacian energy. The role of LNE in structure–property modelling of molecules is demonstrated by statistical approach. The formulation of LNE is not ad hoc; rather, its chemical significance exerts that it outperforms LE in modelling physiochemical behaviours of molecules. Mathematical properties of LN are also revealed by finding crucial bounds of its eigenvalues with characterizing extremal graphs.
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