TY  - JOUR
ID  - Eakawinrujee2022
LB  - Eakawinrujee2022
AU  - Eakawinrujee, Pannawat
AU  - Trakultraipruk, Nantapath
TI  - γ-paired dominating graphs of cycles
ST  - γ-paired dominating graphs of cycles
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 1
SP  - 31
EP  - 54
DO  - https://doi.org/10.7494/OpMath.2022.42.1.31
UR  - https://doi.org/10.7494/OpMath.2022.42.1.31
AB  - 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.
KW  - paired dominating graph
KW  - paired dominating set
KW  - paired domination number
SN  - 1232-9274
ER  -