On maximum independent set of line graphs
Finding a maximum independent set in $L(G)$ is equivalent to finding a maximum matching in $G$. For more, and a fast polynomial-time algorithm that work for e.g., line graphs, see [1].



[1] Lozin, V.V. and Milanič, M., 2008. On finding augmenting graphs. Discrete Applied Mathematics, 156(13), pp.2517-2529.