On Laplacian and distance Laplacian spectra of generalized fan graph and a new graph class

Abstract Given a graph G , the Laplacian matrix of G , L ( G ) is the difference of the adjacency matrix A ( G ) and Deg( G ), where Deg( G ) is the diagonal matrix of vertex degrees. The distance Laplacian matrix D L ( G ) is the difference of the transmission matrix of G and the distance matrix of G . In the given paper, we first obtain the Laplacian and distance Laplacian spectrum of generalized fan graphs. We then introduce a new graph class which is denoted by 𝒩 𝒞 ( F m,n ). Finally, we determine the Laplacian spectrum and the distance Laplacian spectrum of 𝒩 𝒞 ( F m,n ).