@Article{Bednarz2025,
author = "Bednarz, Urszula and Pirga, Mateusz",
title = "(1,2)-PDS in graphs with the small number of vertices of large degrees",
journal = "Opuscula Math.",
year = "2025",
volume = "45",
number = "1",
pages = "53--62",
doi = "https://doi.org/10.7494/OpMath.2025.45.1.53",
url = "https://doi.org/10.7494/OpMath.2025.45.1.53",
abstract = "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 \(n-2\).",
keywords = "domination, secondary domination, neighborhoods, maximum degree",
issn = "1232-9274"
}