Abstract
Let \(G\) be a graph, the Sombor matrix \(S(G)\) of \(G\) was recently introduced by Wang et al. It is a new matrix based on Sombor index, where the \((i,j)\) entry \(S_{ij}=\sqrt{d_i^2+d_j^2}\) if vertices \(i\) and vertices \(j\) are adjacent in \(G\), and \(S_{ij}=0\) for other cases. Xueliang Li and Junming Wang solved the conjecture for the upper and lower bounds of the ABC spectral radius for unicyclic graphs by Ghorbani et al.
Inspired by this, we investigate the spectral radius on Sombor matrix of unicyclic graphs. In the paper, we use the method of classified discussion and Cauchy-Schwartz inequality to determine the external Sombor spectral radius of unicyclic graphs and provide the conditions for the equality.
