For a simple graph G, the following relationships hold: $$RR^T=\Delta+A$$ and $$R^TR=2I+A_{L(G)}$$ where R is the incidence matrix, A is the adjacency matrix, I is the identity matrix, $A_{L(G)}$ is the adjacency of the line graph of G, and $\Delta$ is the diagonal matrix of the vertex degrees; Q, $Q=\Delta+A$, is the signless Laplacian.
Since $RR^T$ and $R^TR$ have the same non-zero eigenvalues,is not the following true? $${\kappa}_l = \sum_{i=1}^n(2+\mu_i)^l$$ where $\kappa_l$ is the $l^{th}$ spectral moment of the signless Laplacian and $\mu_i$ are eigenvalues of the line graph?
UPDATE
$${\kappa}_l = \sum_{i=1}^m(2+\mu_i)^l$$ where m is the number of edges. Now I correctly reproduce the first three spectral moments by use of line graphs.