2018-06-062018-06-062003BARBOSA, Rommel; ELLINGHAM, M. N. A characterisation of cubic parity graphs. Australasian Journal of Combinatorics, Queensland, v. 28, p. 273-293, 2003.e- 2202-3518http://repositorio.bc.ufg.br/handle/ri/15149A graph is Zm-well-covered if all maximal independent sets have the same cardinality modulo m. Zm-well-covered graphs generalise well-covered graphs, those in which all independent sets have the same cardinality. Z2- well-covered graphs are also called parity graphs. A characterisation of cubic well-covered graphs was given by Campbell, Ellingham and Royle. Here we extend this to a characterisation of cubic Zm-well-covered graphs for all integers m ≥ 2; the most interesting case is m = 2, cubic parity graphs. Our main technique involves minimal non-well-covered graphs, and allows us to build our characterisation as an extension of the existing characterisation of cubic well-covered graphs.engAcesso AbertoArtigo