On Second Zagreb Energy of Graphs

Abstract

Chemical structures are transformed into real numbers employing topological indices, which enable numerical computations to substitute pricey wet lab experiments. The spectral properties of topological indices can be investigated by appropriate modification of adjacency matrix. Gutman and Trinajstic, pioneers in the field of chemical graph theory, presented the Zagreb indices, which have governed topological indices research since 1972. The modified adjacency matrix associated to the second Zagreb index (M2) is studied in this work. The second Zagreb energy (ZE2) is generated from this matrix. The application potential of ZE2 is explored by investigating its efficiency in modelling physico-chemical properties of molecules and isomer discrimination. We aim to set up crucial bounds of spectral radius and spread with identifying extremal graphs. Moreover, the ZE2 energy is investigated for numerous special graphs including regular, semi-regular and chain graphs. We construct a divisor type matrix to estimate the M2-spectrum and ZE2 energy of the chain graph.