A note on the upper bound for the paired-domination number of a graph with minimum degree at least two

Networks ◽  
2010 ◽  
pp. n/a-n/a
Author(s):  
Shenwei Huang ◽  
Erfang Shan
Keyword(s):  
Upper Bound ◽  
Minimum Degree ◽  
Domination Number ◽  
Paired Domination Number ◽  
Paired Domination

Bounds on the paired domination number of graphs with minimum degree at least three

2022 ◽  
Vol 417 ◽  
pp. 126782
Author(s):  
Michael A. Henning ◽  
Monika Pilśniak ◽  
Elżbieta Tumidajewicz
Keyword(s):  
Minimum Degree ◽  
Domination Number ◽  
Paired Domination Number ◽  
Paired Domination

Outer-paired domination in graphs

2020 ◽  
Vol 12 (06) ◽  
pp. 2050072
Author(s):  
A. Mahmoodi ◽  
L. Asgharsharghi
Keyword(s):  
Perfect Matching ◽  
Dominating Set ◽  
Domination Number ◽  
Simple Graph ◽  
Minimum Cardinality ◽  
Sharp Bounds ◽  
Paired Domination Number ◽  
Vertex Set ◽  
Paired Domination ◽  
Domination In Graphs

Let [Formula: see text] be a simple graph with vertex set [Formula: see text] and edge set [Formula: see text]. An outer-paired dominating set [Formula: see text] of a graph [Formula: see text] is a dominating set such that the subgraph induced by [Formula: see text] has a perfect matching. The outer-paired domination number of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of an outer-paired dominating set of [Formula: see text]. In this paper, we study the outer-paired domination number of graphs and present some sharp bounds concerning the invariant. Also, we characterize all the trees with [Formula: see text].

scholarly journals An upper bound on the domination number of a graph with minimum degree 2

2009 ◽  
Vol 309 (4) ◽  
pp. 639-646 ◽  
Author(s):  
Allan Frendrup ◽  
Michael A. Henning ◽  
Bert Randerath ◽  
Preben Dahl Vestergaard
Keyword(s):  
Upper Bound ◽  
Minimum Degree ◽  
Domination Number

Paired-domination number of claw-free odd-regular graphs

2016 ◽  
Vol 33 (4) ◽  
pp. 1266-1275
Author(s):  
Wei Yang ◽  
Xinhui An ◽  
Baoyindureng Wu
Keyword(s):  
Domination Number ◽  
Regular Graphs ◽  
Paired Domination Number ◽  
Paired Domination

scholarly journals Upper paired domination versus upper domination

2021 ◽  
Vol vol. 23, no. 3 (Graph Theory) ◽  
Author(s):  
Hadi Alizadeh ◽  
Didem Gözüpek
Keyword(s):  
Perfect Matching ◽  
Dominating Set ◽  
Domination Number ◽  
Graph Classes ◽  
Paired Domination Number ◽  
Upper Domination Number ◽  
Paired Domination ◽  
Cactus Graphs ◽  
Open Question

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.

An improved upper bound on the double Roman domination number of graphs with minimum degree at least two

2019 ◽  
Vol 270 ◽  
pp. 159-167 ◽  
Author(s):  
Rana Khoeilar ◽  
Hossein Karami ◽  
Mustapha Chellali ◽  
Seyed Mahmoud Sheikholeslami
Keyword(s):  
Upper Bound ◽  
Minimum Degree ◽  
Domination Number ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Double Roman Domination
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