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Browsing by Author "Bednarz, Urszula"

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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 $n-2$.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On Fibonacci numbers in edge coloured trees
    (Wydawnictwa AGH, 2017) Bednarz, Urszula; Bród, Dorota; Szynal-Liana, Anetta; Włoch, Iwona; Wołowiec-Musiał, Małgorzata
    In this paper we show the applications of the Fibonacci numbers in edge coloured trees. We determine the second smallest number of all $(A,2B)$-edge colourings in trees. We characterize the minimum tree achieving this second smallest value.