Extension of adjacency matrix in QSPR analysis

The utilization of extended adjacency matrices to investigate various combinatorial properties of graph is one of the most recent research directions in the spectral graph theory. This work proposes a useful modification to the classical adjacency matrix, as well as associated spectral radius and energy. When compared to existing descriptors, the novel energy and Estrada index are established to be significant molecular descriptors in structure-property modelling and isomer discrimination by means of quantitative structure property relationship (QSPR) analysis. Following that, mathematical attributes of the energy are demonstrated by estimating its tight bounds with identifying extremal graphs.