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
Cet article a éte moissonné depuis 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},
year = {2022},
volume = {42},
number = {2},
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 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 %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).