On the first two largest distance Laplacian eigenvalues of unicyclic graphs

The distance Laplacian eigenvalues of a connected graph G are the eigenvalues of its distance Laplacian matrix L(G), defined as L(G)=Tr(G)−D(G), where Tr(G) is the diagonal matrix of vertex transmissions of G, and D(G) is the distance matrix of G. In this paper, we determine the unique unicyclic graphs with maximum largest distance Laplacian eigenvalue and minimum second largest distance Laplacian eigenvalue, respectively.