The Laplacian spectral radius of a class of unicyclic graphs (Q1790098)

Summary: Let \(C(n,k)\) be the set of all unicyclic graphs with \(n\) vertices and cycle length \(k\). For any \(U\in C(n,k)\), \(U\) consists of the (unique) cycle (say \(C_k\)) of length \(k\) and a certain number of trees attached to the vertices of \(C_k\) having (in total) \(n-k\) edges. If there are at most two trees attached to the vertices of \(C_k\), where \(k\) is even, we identify in the class of unicyclic graphs those graphs whose Laplacian spectral radii are minimal.