Equistable simplicial, very well-covered, and line graphs

We verify the conjectures of Mahadev–Peled–Sun and of Orlin, both related to equistable graphs, for the classes of simplicial, very well-covered and line graphs. Our results are based on the combinatorial features of triangle graphs and general partition graphs. In particular, we obtain several equivalent characterizations of equistable simplicial graphs, equistable very well-covered graphs, and equistable line graphs, some of which imply polynomial time recognition algorithms for graphs in these classes.