Bounds for the spectral radius and energy of extended adjacency matrix of graphs

Abstract

© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group. An extend adjacency matrix of a graph (Aex) was introduced decades ago as a precursor for developing a few quite useful molecular topological descriptors. The spectral radius (η1) of the extended adjacency matrix and the extended energy of a graph (εex) have been successfully utilized in QSPR/QSAR investigations. Here, the η1 and εex have been further mathematically analyzed. Several sharp upper bounds for the εex are obtained. In addition, the Nordhaus–Gaddum-type results for the η1 and εex are presented.