Order-sensitive domination in partially ordered sets and graphs


Civan Y., Deniz Z., Yetim M. A.

ORDER, pp.1-16, 2022 (Journal Indexed in SCI Expanded)

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s11083-022-09599-2
  • Title of Journal : ORDER
  • Page Numbers: pp.1-16

Abstract

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∈ D or else a<x<b in P for some a,b∈D for every element x in P which is neither maximal nor minimal, and denote by γ_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 γ_os(P_3(G))=γ_R(G) and γ_os(P_4(G))=2γ(G) hold, where γ(G) and γ_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.