@Article{Eakawinrujee2022,
author = "Eakawinrujee, Pannawat and Trakultraipruk, Nantapath",
title = "γ-paired dominating graphs of cycles",
journal = "Opuscula Math.",
year = "2022",
volume = "42",
number = "1",
pages = "31--54",
doi = "https://doi.org/10.7494/OpMath.2022.42.1.31",
url = "https://doi.org/10.7494/OpMath.2022.42.1.31",
abstract = "A paired dominating set of a graph \(G\) is a dominating set whose induced subgraph contains a perfect matching. The paired domination number, denoted by \(\gamma_{pr}(G)\), is the minimum cardinality of a paired dominating set of \(G\). A \(\gamma_{pr}(G)\)-set is a paired dominating set of cardinality \(\gamma_{pr}(G)\). The \(\gamma\)-paired dominating graph of \(G\), denoted by \(PD_{\gamma}(G)\), as the graph whose vertices are \(\gamma_{pr}(G)\)-sets. Two \(\gamma_{pr}(G)\)-sets \(D_1\) and \(D_2\) are adjacent in \(PD_{\gamma}(G)\) if there exists a vertex \(u\in D_1\) and a vertex \(v\notin D_1\) such that \(D_2=(D_1\setminus \{u\})\cup \{v\}\). In this paper, we present the \(\gamma\)-paired dominating graphs of cycles.",
keywords = "paired dominating graph, paired dominating set, paired domination number",
issn = "1232-9274"
}