Interval Graphs With Alternate Cliques Of Size 3 - Roman Domination Number

References

[1] Allan, R.B. and Laskar, R.C. – On domination, Independent domination numbers of a graph Discrete Math., vol. 23, 1978, pp. 73-76.

[2] Berge, C. – Graphs and Hyperactive graphs, North Holland, Amsterdam in graphs, Networks, vol.10, 1980, pp. 211 – 215.

[3] Cockayne, E.J. and Hedetniemi, S.T. – Towards a theory of domination in graphs. Networks, vol. 7, 1977, pp. 247 -261.

[4] Cockayne, E.J. Dreyer, P.A., Hedetniemi, S.M. and Hedetniemi, S.T. – Roman domination in graphs, Discrete math., vol. 278, 2004, pp. 11 - 22.

[5] Haynes, T.W., Hedetniemi, S.T. and Slater, P.J. – Domination in graphs: Advanced Topics, Marcel Dekkar, Inc., New York, 1998.

[6] Haynes, T.W., Hedetniemi, S.T. and Slater, P.J. – Fundamentals of domination in graphs, Vol. 208 of Monographs and Text books in Pure and Applied Mathematics, Marcel Dekkar, New York, 1998.

[7] Ian Stewart – Defend the Roman Empire!., Scientific American, vol. 281, issue 6, 1999, pp. 136 -139.

[8] Jaya Subba Reddy. C, Reddappa. M and Maheswari.B. – Roman domination in a certain type of interval graph–International Journal of Research and analytical Reviews, vol. 6, issue 1, February 2019, pp. 665–672.

[9] Ore O. – Theory of Graphs, Amer, Math.Soc. Collaq.Publ.38, Providence (1962).

[10] ReValle, C.S. and Rosing K, E. – Defendens imperium romanum: a classical problem in military Strategy, Amer. Math. Monthly, vol.107, issue 7, 2000, pp. 585 -594.

@article{1701656,
      author = {M. Reddappa, C. Jaya Subba Reddy, B. Maheswari},
      title = {Interval Graphs With Alternate Cliques Of Size 3 - Roman Domination Number},
      journal = {Iconic Research And Engineering Journals},
      year = {2019},
      volume = {3},
      number = {4},
      pages = {34-39},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1701656.pdf},
      abstract = {Today graph theory is one of the most flourishing braches of modern mathematics. Graphs are useful in enhancing the understanding of the organization and behavioral characteristics of complex system. The study of domination in graphs originated around 1850 has become the source of interest to the researchers. Interval graphs form a special class of graphs with many interesting properties and revealed their practical relevance for modeling problems arising in the real world. The last 40 years have witnessed a spectacular growth of domination in interval graphs due to its wide range of applications to many fields. Roman domination in graphs is introduced by Cockayne et.al [3, 4] and they studied this concept for various graphs. In this paper a study of Roman domination in Interval graphs with alternate cliques of size 3 is carried out.},
      keywords = {Roman dominating function, Roman domination number, Interval family, Interval graph},
      month = {October},
  }