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A characterization of locating Roman domination edge critical graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 10، شماره 3، آذر 2025، صفحه 531-537 اصل مقاله (368.38 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.29108.1853 | ||
| نویسندگان | ||
| H. Abdollahzadeh Ahangar* 1؛ H. Rahbani1؛ M.R. Sadeghi2 | ||
| 1Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, I.R. Iran | ||
| 2Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, I.R. Iran | ||
| چکیده | ||
| A Roman dominating function (or just \textit{RDF}) on a graph $G =(V, E)$ is a function $f: V \longrightarrow \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$. The weight of an \textit{RDF} $f$ is the value $f(V)=\sum_{u \in {V}}f(u)$. An \textit{RDF} $f$ can be represented as $f=(V_0,V_1,V_2)$, where $V_i=\{v\in V:f(v)=i\}$ for $i=0,1,2$. An \textit{RDF} $f=(V_0,V_1,V_2)$ is called a locating Roman dominating function (or just \textit{L\textit{RDF}}) if $N(u)\cap V_2\neq N(v)\cap V_2$ for any pair $u,v$ of distinct vertices of $V_0$. The locating-Roman domination number $\gamma_R^L(G)$ is the minimum weight of an \textit{L\textit{RDF}} of $G$. A graph $G$ is said to be a locating Roman domination edge critical graph, or just $\gamma_R^L$-edge critical graph, if $\gamma_R^L(G-e)>\gamma_R^L(G)$ for all $e\in E$. The purpose of this paper is to characterize the class of $\gamma_R^L$-edge critical graphs. | ||
| کلیدواژهها | ||
| Roman domination؛ locating Roman domination number؛ critical graph | ||
| 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. https://doi.org/10.1002/net.3230180304
[2] M. Chellali and N. Jafari Rad, Locating-total domination critical graphs., Australas. J. Comb. 45 (2009), 227–234.
[3] R.D. Dutton and R.C. Brigham, On global domination critical graphs, Discrete Math. 309 (2009), no. 19, 5894–5897. https://doi.org/10.1016/j.disc.2008.06.005
[4] W. Goddard, T.W. Haynes, M.A. Henning, and L.C. Van der Merwe, The diameter of total domination vertex critical graphs, Discrete Math. 286 (2004), no. 3, 255–261. https://doi.org/10.1016/j.disc.2004.05.010
[5] P.J.P. Grobler and C.M. Mynhardt, Secure domination critical graphs, Discrete Math. 309 (2009), no. 19, 5820–5827. https://doi.org/10.1016/j.disc.2008.05.050
[6] A. Hansberg, N. Jafari Rad, and L. Volkmann, Characterization of Roman domination critical unicyclic graphs, Util. Math. 86 (2011), 129–146.
[7] A. Hansberg, N. Jafari Rad, and L. Volkmann, Vertex and edge critical Roman domination in graphs, Util. Math. 92 (2013), 73–88. [8] T.W. Haynes, S. Hedetniemi, and P. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc. New York, 1998.
[9] N. Jafari Rad, Critical concept for 2-rainbow domination in graphs, Australas. J. Comb. 51 (2011), 49–60.
[10] N. Jafari Rad, Roman domination critical graphs upon edge subdivision, J. Combin. Math. Combin. Comput. 93 (2015), 227–245.
[11] N. Jafari Rad and H. Rahbani, Bounds on the locating Roman domination number in trees, Discuss. Math. Graph Theory 38 (2018), no. 1, 49–62. http://doi.org/10.7151/dmgt.1989
[12] N. Jafari Rad, H. Rahbani, and L. Volkmann, Locating Roman domination in graphs, Util. Math. 110 (2019), 203–222.
[13] P.J. Slater, Domination and location in acyclic graphs, Networks 17 (1987), no. 1, 55–64. https://doi.org/10.1002/net.3230170105
[14] P.J. Slater, Dominating and reference sets in graphs, J. Math. Phys. Sci 22 (1988), 445–455.
[15] I. Stewart, Defend the Roman empire!, Scientific American 281 (1999), no. 6, 136–138. | ||
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