Geodesic
A note on total and paired domination of Cartesian product graphs
The electronic journal of combinatorics, Tome 20 (2013) no. 3
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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 $A^n$.
DOI : 10.37236/2535
Classification : 05C69, 05C76
Mots-clés : Vizing's conjecture, dominating set, domination number 
@article{10_37236_2535,
     author = {K. Choudhary and S. Margulies and I. V. Hicks},
     title = {A note on total and paired domination of {Cartesian} product graphs},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {3},
     doi = {10.37236/2535},
     zbl = {1298.05245},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2535/}
}
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K. Choudhary; S. Margulies; I. V. Hicks. A note on total and paired domination of Cartesian product graphs. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/2535

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