Article in volume
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Title:
Corrigendum to: independent transversal domination in graphs [Discuss. Math. Graph Theory 32 (2012) 5-17]
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Discussiones Mathematicae Graph Theory 42(2) (2022) 601-611
Received: 2019-05-29 , Revised: 2020-01-03 , Accepted: 2020-01-03 , Available online: 2020-01-29 , https://doi.org/10.7151/dmgt.2297
Abstract:
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 $|X|\leq |Y|$ and $|X|=\gamma(G)$,
then $\gamma_{it}(G)=\gamma(G)+1$ 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
References:
- 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 - J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London, 1976).
- G. Chartrand and L. Lesniak, Graphs and Digraphs, Fourth Edition (CRC Press, Boca Raton, 2005).
- I.S. Hamid, Independent transversal domination in graphs, Discuss. Math. Graph Theory 32 (2012) 5–17.
https://doi.org/10.7151/dmgt.1581 - T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
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