Given a graph $G$, the Laplacian matrix of $G$, $L(G)$ is the difference of the adjacency matrix $A(G)$ and $\text{ Deg}(G)$, where $\text{ Deg}(G)$ 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 $\mathcal{ NC}(F_{ m,n})$. Finally, we determine the Laplacian spectrum and the distance Laplacian spectrum of $\mathcal{ NC}(F_{ m,n})$.
Categories: math.CO