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This paper characterizes graphs whose entire power sequence exhibits the well-covered property, meaning every independent set is maximal. Complete classifications are provided for chordal, cochordal, and very well-covered graphs, establishing structural conditions for this property. The findings contribute to a deeper understanding of graph covering properties and their preservation under graph powers.
Every power of a chordal graph is well-covered, a property not shared by all graph classes.
In this paper, we investigate graphs with the property that all of their powers are well-covered. We obtain complete classifications for several graph classes, including chordal graphs, cochordal graphs, and very well-covered graphs.