Characterization of Zm-well-covered graphs for some classes of graphs

A graph G is a Zm-well-covered graph if |I1|≡|I2|(mod m) for all maximal independent sets I1 and I2 in V(G) [3]. The recognition problem of Zm-well-covered graphs is a Co-NP-Complete problem. We give a characterization of Zm-well-covered graphs for chordal, simplicial and circular arc graphs.