Produtos de grafos Zm-bem-cobertos

a graph is zm-well-covered if |i| ≡ |j| (mod m), for all i, j maximal independent sets in v(g). a graph g is strongly zm-well-covered if g is a zm-well-covered graph and g\{e} is zm-well-covered, ？ e ∈ e(g). a graph g is zm-well-covered if g is zm-well-covered and g\{v} is zm-well-covered, ？ e ∈ v(g). we prove that k1 and k2 are the only 1-zm-well-covered graphs with girth > 6. they are also the only ones with girth > and strongly zm-well-covered. we show a necessary and sufficient condition for the lexicographic product of graphs to be a zm-well-covered one and some properties for the cartesian product of cycles.