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

A connected graph G is a cactus if any two of its cycles have at most one common vertex. Denote by  /></span> the set of <i>n</i>-vertex cacti with matching number <i>q</i>. Huang, Deng and Simi? 23] identified the unique graph with the maximum spectral radius among 2<i>q</i>-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 <span class= /></span> are determined. Consequently, the first two largest spectral radii together with cacti having perfect matchings are also determined.</td>
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Keywords:05C50  15A18
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