The Laplacian Spectral Radius of a Class of Unicyclic Graphs

Abstract

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.