On the neighbourhood degree sum-based Laplacian energy of graphs

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