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Browsing by Subject "maximum degree"

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    Item type:Article, Access status: Open Access ,
    (1,2)-PDS in graphs with the small number of vertices of large degrees
    (Wydawnictwa AGH, 2025) Bednarz, Urszula; Pirga, Mateusz
    We define and study a perfect $(1,2)$-dominating set which is a special case of a $(1,2)$-dominating set. We discuss the existence of a perfect $(1,2)$-dominating set in graphs with at most two vertices of maximum degree. In particular, we present a complete solution if the maximum degree equals $n-1$ or $n-2$.