Geodesic
Upper paired domination versus upper domination
Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 3.

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A paired dominating set $P$ is a dominating set with the additional property that $P$ has a perfect matching. While the maximum cardainality of a minimal dominating set in a graph $G$ is called the upper domination number of $G$, denoted by $\Gamma(G)$, the maximum cardinality of a minimal paired dominating set in $G$ is called the upper paired domination number of $G$, denoted by $\Gamma_{pr}(G)$. By Henning and Pradhan (2019), we know that $\Gamma_{pr}(G)\leq 2\Gamma(G)$ for any graph $G$ without isolated vertices. We focus on the graphs satisfying the equality $\Gamma_{pr}(G)= 2\Gamma(G)$. We give characterizations for two special graph classes: bipartite and unicyclic graphs with $\Gamma_{pr}(G)= 2\Gamma(G)$ by using the results of Ulatowski (2015). Besides, we study the graphs with $\Gamma_{pr}(G)= 2\Gamma(G)$ and a restricted girth. In this context, we provide two characterizations: one for graphs with $\Gamma_{pr}(G)= 2\Gamma(G)$ and girth at least 6 and the other for $C_3$-free cactus graphs with $\Gamma_{pr}(G)= 2\Gamma(G)$. We also pose the characterization of the general case of $C_3$-free graphs with $\Gamma_{pr}(G)= 2\Gamma(G)$ as an open question.
DOI : 10.46298/dmtcs.7331
Classification : 05C69 
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     author = {Alizadeh, Hadi and G\"oz\"upek, Didem},
     title = {Upper paired domination versus upper domination},
     journal = {Discrete mathematics & theoretical computer science},
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     number = {3},
     year = {2021-2022},
     doi = {10.46298/dmtcs.7331},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.7331/}
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Alizadeh, Hadi; Gözüpek, Didem. Upper paired domination versus upper domination. Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 3. doi : 10.46298/dmtcs.7331. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.7331/

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