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

An extend adjacency matrix of a graph (A(ex)) was introduced decades ago as a precursor for developing a few quite useful molecular topological descriptors. The spectral radius (eta(1)) of the extended adjacency matrix and the extended energy of a graph (epsilon(ex)) have been successfully utilized in QSPR/QSAR investigations. Here, the eta(1) and epsilon(ex) have been further mathematically analyzed. Several sharp upper bounds for the epsilon(ex) are obtained. In addition, the Nordhaus-Gaddum-type results for the eta(1) and epsilon(ex) are presented.

Automated summary

The extended adjacency matrix of a graph was introduced as a precursor for developing molecular topological descriptors, with the spectral radius and extended energy successfully utilized in QSPR/QSAR investigations. The study further analyzed the mathematical properties of these descriptors, obtaining sharp upper bounds for the extended energy and presenting Nordhaus-Gaddum-type results for the spectral radius and extended energy.