edge dominating set

subset of a graph's edges such that all other edges are adjacent to it

en-US/ˈɛd͡ʒ ˈdɑməˌneɪdɪŋ ˈsɛt/
en-GB/ˈɛd͡ʒ ˈdɒmɪneɪtɪŋ ˈsɛt/

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set