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

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).