The laplacian spectral radius of a class of unicyclic graphs

Let c (n,k) be the set of all unicyclic graphs with n vertices and cycle length k. for any u ∈ c (n,k),u consists of the (unique) cycle (say ck) of length k and a certain number of trees attached to the vertices of ck having (in total) n - k edges. if there are at most two trees attached to the vertices of ck,where k is even,we identify in the class of unicyclic graphs those graphs whose laplacian spectral radii are minimal. © 2013 haixia zhang.