Independent protection in graphs

We show that any well-covered graph (i.e., all maximal independent sets have the same cardinality k) is k-i-protectable, even cycles in general are 1-i-protectable but not 2-i-protectable, and odd cycles in general are 2-i-protectable but not 3-i-protectable. We characterize k-i-protectable trees and give methods to construct larger k-i-protectable graphs from smaller ones.