On graphs with distance Laplacian spectral radius of multiplicity n − 3

Let ∂1L≥∂2L≥⋯≥∂nL be the distance Laplacian eigenvalues of a connected graph G and m(∂iL) the multiplicity of ∂iL. It is well known that the graphs with m(∂1L)=n−1 are complete graphs. Recently, the graphs with m(∂1L)=n−2 have been characterised by Celso et al. In this paper, we completely determine the graphs with m(∂1L)=n−3.