Garijo et al.'s locating-dominating set conjecture for twin-free graphs
Let be a twin-free graph of order without isolated vertices. A locating-dominating set is a dominating set such that every two distinct vertices outside have distinct neighborhoods in ; let denote the minimum cardinality of a locating-dominating set of .
Garijo et al.'s conjecture. Every twin-free graph of order without isolated vertices satisfies
This conjecture proposes a universal upper bound on the locating-dominating number of twin-free graphs. The supplied source does not indicate whether the conjecture has been resolved.
References
Primary source
Florent Foucaud, Michael A. Henning, Christian Löwenstein and Thomas Sasse, “Locating-dominating sets in twin-free graphs”, arXiv:1412.2376 (2015).
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