The least eigenvalue of unicyclic graphs with n vertices and k pendant vertices

Let U(n,k) be the set of unicyclic graphs with n vertices and k pendant vertices. In this paper, we determine the unique graph with the minimal least eigenvalue among all graphs in U(n,k). The work is related with that of Guo [S.G. Guo, The spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices, Linear Algebra Appl. 408 (2005) 78–85], which determined the unicyclic graph with the maximal spectral radius in U(n,k). We can observe that the extremal graph on the least eigenvalue is different from that on the spectral radius.