The least eigenvalues of the signless Laplacian of non-bipartite graphs with pendant vertices

Abstract: In this paper, we determine the graph whose least eigenvalue of the 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 the signless Laplacian of a graph in terms of the number of pendant vertices. [Copyright &y& Elsevier]