Seymour's Second-Neighborhood Conjecture states that every directed graph whose underlying graph is simple has at least one vertex (Formula presented.) such that the number of vertices of out-distance two from (Formula presented.) is at least as large as the number of vertices of out-distance one from it. We present alternative statements of the conjecture in the language of linear algebra.
Publication Source (Journal or Book title)
Journal of Graph Theory
Bouya, F., & Oporowski, B. (2021). Seymour's second-neighborhood conjecture from a different perspective. Journal of Graph Theory, 97 (3), 393-400. https://doi.org/10.1002/jgt.22661