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