  There is a class of graphs with well-covered dimension equal to the
simplicial clique number that contains all chordal graphs and infinitely many
other graphs. These graphs generalize a result by Brown and Nowakowski on the
well-covered dimension of chordal graphs. Furthermore, each member of the
infinite family of Sierpinski gasket graphs of order at least $2$ has
well-covered dimension $3,$ the simplicial clique number.
