Order-Sensitive Domination in Partially Ordered Sets and Graphs
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Dosyalar
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
For a (finite) partially ordered set (poset) P, we call a dominating set D in the comparability graph of P, an order-sensitive dominating set in P if either x is an element of D or else a < x < b in P for some a,b is an element of D for every element x in P which is neither maximal nor minimal, and denote by gamma(os)(P), the least size of an order-sensitive dominating set of P. For every graph G and integer k >= 2, we associate to G a graded poset P-k(G) of height k, and prove that gamma(os)(P-3(G)) = gamma(R)(G) and gamma(os)(P-4(G)) = 2 gamma(G) hold, where gamma(G) and gamma(R)(G) are the domination and Roman domination number of G respectively. Moreover, we show that the order-sensitive domination number of a poset P exactly corresponds to the biclique vertex-partition number of the associated bipartite transformation of P.
Açıklama
Anahtar Kelimeler
Domination; Partially Ordered Set; Order-Sensitive; Comparability; Roman Domination; Biclique Vertex-Partition
Kaynak
Order-A Journal on The Theory of Ordered Sets and Its Applications
WoS Q Değeri
Q4
Scopus Q Değeri
Q3
