A characterization of Z m -well-covered graphs of girth 6 or more

Abstract

The class of Zm-well-covered graphs, those in which the cardinality of every maximal independent subset of vertices is congruent to the same number modulo m, contains the well-covered graphs as well as parity graphs. Here we consider such graphs, where there is no small cycle present and obtain a characterization for those of girth 6 or more. Weighted well-covered graphs of girth 7 or more are also characterized, and this result is used, in turn, to characterize magic well-covered graphs of girth 7 or more. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 246–255, 2000