On Maximal Det-Independent (Res-Independent) Sets in Graphs
نویسندگان
چکیده
In this writing, we point out some errors made in Boutin (Graphs Combin 25:789–806, 2009), where the author claims that a maximal independent set hereditary system is minimal determining (resolving) set. Further more, if exchange property holds at level of resolving sets, then, corresponding matroid. We give counter examples to disprove both her claims. Besides, prove there exist graphs having such sets which are not necessarily sets. Also, necessary and sufficient conditions for class have (resolving).
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2022
ISSN: ['1435-5914', '0911-0119']
DOI: https://doi.org/10.1007/s00373-021-02452-0