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

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