Potential Laplacian variant of graphs

The spectral graph theory plays a crucial role in representing graph theoretic information employing algebraic properties of specific matrices. Adjacency (A) and Laplacian (L) matrices are the most important tools in this discipline for uncovering thousands of secrets about graph theory and its applications. A massive amount of works on these matrices led to a contemporary trend of modifying them. The NBD Laplacian matrix LN is proposed here as a useful extension of L. Fascinating mathematical features of LN are revealed by finding crucial bounds of its eigenvalues with characterizing extremal graphs. Role of this matrix spectrum in structure–property modelling of molecules is also demonstrated. The formulation of LN matrix is not ad hoc; rather, its chemical significance exerts that it outperforms L in explaining physico-chemical properties of molecules and isomer discrimination, which is quite encouraging.