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A counterexample to a conjecture of Jafari Rad and Volkmann | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 9، دوره 7، شماره 1، شهریور 2022، صفحه 91-92 اصل مقاله (247.43 K) | ||
| نوع مقاله: Short notes | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27226.1214 | ||
| نویسندگان | ||
| Mostafa Blidia؛ Mustapha Chellali* | ||
| Department of Mathematics, University of Blida 1. B.P. 270, Blida, Algeria | ||
| چکیده | ||
| In this short note, we disprove the conjecture of Jafari Rad and Volkmann that every $\gamma $-vertex critical graph is $\gamma _{R}$-vertex critical, where $\gamma (G)$ and $\gamma _{R}(G)$ stand for the domination number and the Roman domination number of a graph $G$, respectively. | ||
| کلیدواژه‌ها | ||
| γ -vertex critical graphs؛ γ _{R}-vertex critical graphs؛ Roman domination | ||
| مراجع | ||
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[1] R.C. Brigham, P.Z. Chinn, and R.D. Dutton, Vertex domination-critical graphs, Networks 18 (1988), no. 3, 173–179.
[2] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, Roman domination in graphs, Topics in Domination in Graphs (T.W. Haynes, S.T. Hedetniemi, and M.A. Henning, eds.), Springer International Publishing, Berlin, 2020, pp. 365– 409. [3] N. Jafari Rad, A. Hansberg, and L. Volkmann, Vertex and edge critical Roman domination in graphs, Util. Math. 92 (2013), 73–88.
[4] N. Jafari Rad and L. Volkmann, Changing and unchanging the Roman domination number of a graph, Util. Math. 89 (2012), 79–95. | ||
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