The least eigenvalues of signless Laplacian of non-bipartite graphs with   pendant vertices
  In this paper we determine the graph whose least eigenvalue of signless Laplacian attains the minimum or maximum among all connected non-bipartite graphs of fixed order and given number of pendant vertices. Thus we obtain a lower bound and an upper bound for the least eigenvalue of signless Laplacian of a graph in terms of the number of pendent vertices. 
Yi-Zheng Fan, Yi Wang, Huan Guo
math.CO