Original Articles

Ordering n-vertex cacti with matching number q by their spectral radii

Published in: Quaestiones Mathematicae
Volume 37 , issue 3 , 2014 , pages: 401–414

DOI: 10.2989/16073606.2013.779612

Author(s): Ailin Hou School of Medical Imaging, P.R. China , Shuchao Li Faculty of Mathematics and Statistics, P.R. China

Keywords: 05C50 , 15A18 , 05C50 , 15A18

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Abstract

A connected graph G is a cactus if any two of its cycles have at most one common vertex. Denote by the set of n-vertex cacti with matching number q. Huang, Deng and Simić [23] identified the unique graph with the maximum spectral radius among 2q-vertex cacti with perfect matchings. In this paper, as a continuance of it, the largest and second largest spectral radii together with the corresponding graphs among are determined. Consequently, the first two largest spectral radii together with cacti having perfect matchings are also determined.

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