Bounds for the spectral radius and energy of extended adjacency matrix of graphs. Issue 10 (27th July 2021)

• Record Type: Journal Article
• Authors: Wang, Zhao; Mao, Yaping; Furtula, Boris; Wang, Xu
• Is Part Of: Linear & multilinear algebra. Volume 69:Issue 10(2021)
• Page Start: 1813
• Page End: 1824
• Publication Date: 2021-07-27
• Subjects: Graph spectra -- extended adjacency matrix -- extended spectral radius -- extended energy -- Nordhaus–Gaddum-type results; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1641464
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: 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.