In connected graphs the number of min-forced vertices is at most (2/3)(n minus the size of a minimum locating-dominating code), implying a maximum ratio of 2/5 attained by certain paths, and deciding whether a vertex is min-forced is co-NP-hard.
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New Results on Vertices that Belong to Every Minimum Locating-Dominating Code
In connected graphs the number of min-forced vertices is at most (2/3)(n minus the size of a minimum locating-dominating code), implying a maximum ratio of 2/5 attained by certain paths, and deciding whether a vertex is min-forced is co-NP-hard.