Geodesic
Corrigendum to: Independent Transversal Domination in Graphs [Discuss. Math. Graph Theory 32 (2012) 5–17]
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 2, pp. 601-611.

Voir la notice de l'article provenant de la source Library of Science

In [Independent transversal domination in graphs, Discuss. Math. Graph Theory 32 (2012) 5–17], Hamid claims that if G is a connected bipartite graph with bipartition X, Y such that |X| ≤ |Y| and |X| = γ(G), then γit(G) = γ(G) + 1 if and only if every vertex x in X is adjacent to at least two pendant vertices. In this corrigendum, we give a counterexample for the sufficient condition of this sentence and we provide a right characterization. On the other hand, we show an example that disproves a construction which is given in the same paper.
Keywords: domination, independent, transversal, covering, matching 
@article{DMGT_2022_42_2_a15,
     author = {Guzman-Garcia, Emma and S\'anchez-L\'opez, Roc{\'\i}o},
     title = {Corrigendum to: {Independent} {Transversal} {Domination} in {Graphs} {[Discuss.} {Math.} {Graph} {Theory} 32 (2012) 5{\textendash}17]},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {601--611},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2022_42_2_a15/}
}
TY  - JOUR
AU  - Guzman-Garcia, Emma
AU  - Sánchez-López, Rocío
TI  - Corrigendum to: Independent Transversal Domination in Graphs [Discuss. Math. Graph Theory 32 (2012) 5–17]
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2022
SP  - 601
EP  - 611
VL  - 42
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2022_42_2_a15/
LA  - en
ID  - DMGT_2022_42_2_a15
ER  - 
%0 Journal Article
%A Guzman-Garcia, Emma
%A Sánchez-López, Rocío
%T Corrigendum to: Independent Transversal Domination in Graphs [Discuss. Math. Graph Theory 32 (2012) 5–17]
%J Discussiones Mathematicae. Graph Theory
%D 2022
%P 601-611
%V 42
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2022_42_2_a15/
%G en
%F DMGT_2022_42_2_a15
Guzman-Garcia, Emma; Sánchez-López, Rocío. Corrigendum to: Independent Transversal Domination in Graphs [Discuss. Math. Graph Theory 32 (2012) 5–17]. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 2, pp. 601-611. http://geodesic.mathdoc.fr/item/DMGT_2022_42_2_a15/

[1] H.A. Ahangar, V. Samodivkin and I.G. Yero, Independent transversal dominating sets in graphs: Complexity and structural properties, Filomat 30 (2016) 293–303. https://doi.org/10.2298/FIL1602293A

[2] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London, 1976).

[3] G. Chartrand and L. Lesniak, Graphs and Digraphs, Fourth Edition (CRC Press, Boca Raton, 2005).

[4] I.S. Hamid, Independent transversal domination in graphs, Discuss. Math. Graph Theory 32 (2012) 5–17. https://doi.org/10.7151/dmgt.1581

[5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).