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For biomedical researchers to fulfill their responsibility for protecting the environment, they must do more than meet the scientific challenge of reducing the number and volume of hazardous materials used in their laboratories and the engineering challenge of reducing pollution and shifting to cleaner energy sources. They must also meet the public… (More)
Unique minimum vertex dominating sets in the Cartesian product of a graph with a complete graph are considered. We first give properties of such sets when they exist. We then show that when the first factor of the product is a tree, consideration of the tree alone is sufficient to determine if the product has a unique minimum dominating set.