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All issues Volume 59 / No 2 (March-April 2025) RAIRO-Oper. Res., 59 2 (2025) 1247-1256 References
Open Access
Issue
RAIRO-Oper. Res.
Volume 59, Number 2, March-April 2025
Page(s) 1247 - 1256
DOI https://doi.org/10.1051/ro/2025039
Published online 06 May 2025
  • A. Alhashim, W.J. Desormeaux and T.W. Haynes, Roman domination in complementary prisms. Aus. J. Comb. 68 (2017) 218–228. [Google Scholar]
  • S. Banerjee, J.M. Keil and D. Pradhan, Perfect Roman domination in graphs. Theor. Comput. Sci. 796 (2019) 1–21. [CrossRef] [Google Scholar]
  • L.A. Basilio, S. Bermudo and J.M. Sigarreta, Bounds on the differential of a graph. Utilitas Mathematica 103 (2017) 319–334. [MathSciNet] [Google Scholar]
  • Z.N. Berberler and M. Çerezci, Unique response Roman domination versus 2-packing differential in complementary prisms. Math. Notes 115 (2024) 868–876. [CrossRef] [MathSciNet] [Google Scholar]
  • Z.N. Berberler and A. Kanlı, Differential in complementary prisms. Numer. Methods Part. Differ. Equ. 38 (2022) 936–946. [CrossRef] [Google Scholar]
  • Z.N. Berberler and A. Kanlı, Roman domination in complementary prisms. MAT-KOL 30 (2024) 133–140. [Google Scholar]
  • S. Bermudo, On the differential and Roman domination number of a graph with minimum degree two. Discrete Appl. Math. 232 (2017) 64–72. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Bermudo and H. Fernau, Lower bounds on the differential of a graph. Discrete Math. 312 (2012) 3236–3250. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Bermudo and H. Fernau, Computing the differential of a graph: hardness, approximability and exact algorithms. Discrete Appl. Math. 165 (2014) 69–82. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Bermudo and H. Fernau, Combinatorics for smaller kernels: the differential of a graph. Theor. Comput. Sci. 562 (2015) 330–345. [CrossRef] [Google Scholar]
  • S. Bermudo, H. Fernau and J.M. Sigarreta, The differential and the Roman domination number of a graph. Appl. Anal. Discrete Math. 8 (2014) 155–171. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Bermudo, J.C. Hernández-Gómez, J.M. Rodríguez and J.M. Sigarreta, Relations between the differential and parameters in graphs. Electron. Notes Discrete Math. 46 (2014) 281–288. [CrossRef] [Google Scholar]
  • S. Bermudo, L. De la Torre, A.M. Martín-Caraballo and J.M. Sigarreta, The differential of the strong product graphs. Int. J. Comput. Math. 92 (2015) 1124–1134. [CrossRef] [MathSciNet] [Google Scholar]
  • S. Bermudo, J.M. Rodríguez and J.M. Sigarreta, On the differential in graphs. Utilitas Mathematica 97 (2015) 257–270. [MathSciNet] [Google Scholar]
  • J.A. Bondy and U.S.R Murty, Graph Theory with Applications. American Elsevier Publishing Co., Inc., New York (1976). [CrossRef] [Google Scholar]
  • F. Buckley and F. Harary, Distance in Graphs. Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA (1990). [Google Scholar]
  • A. Cabrera Martínez and J.A. Rodríguez-Velázquez, On the perfect differential of a graph. Quaestiones Mathematicae 45 (2021) 327–345. [Google Scholar]
  • B. Chaluvaraju and V. Chaitra, Roman domination in complementary prism graphs. Int. J. Math. Comb. 2 (2012) 24–31. [Google Scholar]
  • G. Chartrand and L. Lesniak, Graphs and Digraphs, 4th edition. Chapman Hall, London (2005). [Google Scholar]
  • E.J. Cockayne, P.A. Dreyer, S.M. Hedetniemi and S.T. Hedetniemi, Roman domination in graphs. Discrete Math. 278 (2004) 11–22. [Google Scholar]
  • M. Darkooti, A. Alhevaz, S. Rahimi and H. Rahbani, On perfect Roman domination number in trees: complexity and bounds. J. Comb. Optim. 38 (2019) 712–720. [CrossRef] [MathSciNet] [Google Scholar]
  • P.A. Dreyer, Applications and variations of domination in graphs. Ph.D. thesis, Rutgers University, New Jersey (2000). [Google Scholar]
  • R. Frucht and F. Harary, On the corona of two graphs. Aequ. Math. 4 (1970) 322–325. [CrossRef] [Google Scholar]
  • X. Fu, Y. Yang and B. Jiang, Roman domination in regular graphs. Discrete Math. 309 (2009) 1528–1537. [CrossRef] [MathSciNet] [Google Scholar]
  • T.W. Haynes, S. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs. Marcel Dekker, New York (1998). [Google Scholar]
  • T.W. Haynes, M.A. Henning, P.J. Slater and L.C. Van Der Merwe, The complementary product of two graphs. Bull. Inst. Comb. App. 51 (2007) 21–30. [Google Scholar]
  • M.A. Henning, A characterization of Roman trees. Discuss. Math. Graph Theory 22 (2002) 225–234. [Google Scholar]
  • M.A. Henning and W.F. Klostermeyer, Perfect Roman domination in regular graphs. Appl. Anal. Discrete Math. 12 (2018) 143–152. [CrossRef] [MathSciNet] [Google Scholar]
  • M.A. Henning, W.F. Klostermeyer and G. MacGillivray, Perfect Roman domination in trees. Discrete Appl. Math. 236 (2018) 235–245. [CrossRef] [MathSciNet] [Google Scholar]
  • J.C. Hernández-Gómez, Differential and operations on graphs. Int. J. Math. Anal. 9 (2015) 341–349. [CrossRef] [Google Scholar]
  • J.R. Lewis, Differentials of graphs. Master’s thesis, East Tennessee State University (2004). [Google Scholar]
  • M. Liedloff, T. Kloks, J. Liu and S.-L. Peng, Efficient algorithms on Roman domination on some classes of graphs. Discrete Appl. Math. 156 (2008) 3400–3415. [CrossRef] [MathSciNet] [Google Scholar]
  • K. Mann and H. Fernau, Perfect Roman domination: aspects of enumeration and parameterization. Algorithms 17 (2024) 576. [CrossRef] [Google Scholar]
  • J.L. Mashburn, T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi and P.J. Slater, Differentials in graphs. Utilitas Mathematica 69 (2006) 43–54. [MathSciNet] [Google Scholar]
  • D.A. Mojdeh, A. Parsian and I. Masoumi, Strong Roman domination number of complementary prism graphs. Turkish J. Math. Comput. Sci. 11 (2019) 40–47. [Google Scholar]
  • P. Pavlič and J. Žerovnik, Roman domination number of the Cartesian products of paths and cycles. Electron. J. Comb. 19 (2012) 1–37. [Google Scholar]
  • P.R.L. Pushpam and D. Yokesh, Differential in certain classes of graphs. Tamkang J. Math. 41 (2010) 129–138. [CrossRef] [MathSciNet] [Google Scholar]
  • W. Shang and X. Hu, The Roman domination problem in unit disk graphs. Lect. Notes Comput. Sci. 4489 (2007) 305–312. [CrossRef] [Google Scholar]
  • J.M. Sigarreta, Differential in Cartesian product graphs. Ars Comb. 126 (2016) 259–267. [Google Scholar]
  • X. Song and W. Shang, Roman domination in a tree. Ars Comb. 98 (2011) 73–82. [Google Scholar]
  • I. Stewart, Defned the Roman Empire. Scientific American (1999) 136–139. [Google Scholar]
  • D.B. West, Introduction to Graph Theory. Prentice Hall, NJ (2001). [Google Scholar]
  • J. Yue and J. Song, Note on the perfect Roman domination number of graphs. Appl. Math. Comput. 364 (2020) 124685. [CrossRef] [MathSciNet] [Google Scholar]

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