scholarly journals Paired-domination

1998 ◽  
Vol 18 (1) ◽  
pp. 63 ◽  
Author(s):  
Shannon L. Fitzpatrick ◽  
Bert L. Hartnell
Keyword(s):  
Paired Domination

scholarly journals A Note on the Paired-Domination Subdivision Number of Trees

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 181 ◽  
Author(s):  
Xiaoli Qiang ◽  
Saeed Kosari ◽  
Zehui Shao ◽  
Seyed Mahmoud Sheikholeslami ◽  
Mustapha Chellali ◽  
...  
Keyword(s):  
Upper Bound ◽  
Isolated Vertex ◽  
Paired Domination ◽  
Domination Subdivision Number

For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star), then sdγpr(T)≤min{γpr(T)2+1,n2}, improving the (n−1)-upper bound that was recently proven.

scholarly journals A Note on Total and Paired Domination of Cartesian Product Graphs

10.37236/2535 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
K. Choudhary ◽  
S. Margulies ◽  
I. V. Hicks
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Cartesian Product ◽  
Minimum Dominating Set ◽  
Cartesian Product Of Graphs ◽  
Product Graphs ◽  
Cartesian Product Graphs ◽  
Paired Domination ◽  
Product Of Graphs

A dominating set $D$ for a graph $G$ is a subset of $V(G)$ such that any vertex not in $D$ has at least one neighbor in $D$. The domination number $\gamma(G)$ is the size of a minimum dominating set in G. Vizing's conjecture from 1968 states that for the Cartesian product of graphs $G$ and $H$, $\gamma(G)\gamma(H) \leq \gamma(G \Box H)$, and Clark and Suen (2000) proved that $\gamma(G)\gamma(H) \leq 2 \gamma(G \Box H)$. In this paper, we modify the approach of Clark and Suen to prove a variety of similar bounds related to total and paired domination, and also extend these bounds to the $n$-Cartesian product of graphs $A^1$ through $A^n$.

scholarly journals Complexity of distance paired-domination problem in graphs

2012 ◽  
Vol 459 ◽  
pp. 89-99 ◽  
Author(s):  
Gerard J. Chang ◽  
B.S. Panda ◽  
D. Pradhan
Keyword(s):  
Domination Problem ◽  
Paired Domination

Paired-Domination Problem on Distance-Hereditary Graphs

Algorithmica ◽  
2020 ◽  
Vol 82 (10) ◽  
pp. 2809-2840
Author(s):  
Ching-Chi Lin ◽  
Keng-Chu Ku ◽  
Chan-Hung Hsu
Keyword(s):  
Domination Problem ◽  
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 The diameter of paired-domination vertex critical graphs

2008 ◽  
Vol 58 (4) ◽  
pp. 887-897 ◽  
Author(s):  
Michael A. Henning ◽  
Christina M. Mynhardt
Keyword(s):  
Critical Graphs ◽  
Paired Domination

scholarly journals Distance paired domination numbers of graphs

2008 ◽  
Vol 308 (12) ◽  
pp. 2473-2483 ◽  
Author(s):  
Joanna Raczek
Keyword(s):  
Paired Domination ◽  
Domination Numbers
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