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Total Roman Domination in an Interval Graph with Alternate Cliques of Size 3

M. Reddappa, C. Jaya Subba Reddy, B. Maheswari in Applied Mathematics

International Journal of Applied Information Systems
Year of Publication: 2019
Publisher: Foundation of Computer Science (FCS), NY, USA
Authors:M. Reddappa, C. Jaya Subba Reddy, B. Maheswari
10.5120/ijais2019451836
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  1. M Reddappa, Jaya Subba C Reddy and B Maheswari. Total Roman Domination in an Interval Graph with Alternate Cliques of Size 3. International Journal of Applied Information Systems 12(26):16-22, December 2019. URL, DOI BibTeX

    @article{10.5120/ijais2019451836,
    	author = "M. Reddappa and C. Jaya Subba Reddy and B. Maheswari",
    	title = "Total Roman Domination in an Interval Graph with Alternate Cliques of Size 3",
    	journal = "International Journal of Applied Information Systems",
    	issue_date = "December, 2019",
    	volume = 12,
    	number = 26,
    	month = "December",
    	year = 2019,
    	issn = "2249-0868",
    	pages = "16-22",
    	url = "http://www.ijais.org/archives/volume12/number26/1074-2019451836",
    	doi = "10.5120/ijais2019451836",
    	publisher = "Foundation of Computer Science (FCS), NY, USA",
    	address = "New York, USA"
    }
    

Abstract

The theory of Graphs is an important branch of Mathematics that was developed exponentially. The theory of domination in graphs is rapidly growing area of research in graph theory today. It has been studied extensively and finds applications to various branches of Science & Technology.

Interval graphs have drawn the attention of many researchers for over 40 years. They form a special class of graphs with many interesting properties and revealed their practical relevance for modeling problems arising in the real world. The theory of domination in graphs introduced by Ore [12] and Berge [4] has been ever green of graph theory today. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et.al. [1, 2].

In this paper a study of total domination and total Roman domination number of an interval graph with alternate cliques of size 3 is carried out.

Reference

  1. Haynes, T.W., Hedetniemi, S.T., and Slater, P.J. 1998. Domination in graphs: Advanced Topics, Marcel Dekkar, Inc., New York.
  2. Haynes, T.W., Hedetniemi, S.T., and Slater, P.J.1998. Fundamentals of domination in graphs, Marcel Dekkar, Inc., New York.
  3. Allan, R.B. and Laskar, R.C. 1978. On domination, Independent domination numbers of a graph Discrete Math., 23, 73-76.
  4. Berge, C. 1980. Graphs and Hyperactive graphs, North Holland, Amsterdam in graphs, Networks, 10,211 – 215.
  5. Cockayne, E.J. and Hedetniemi, S.T. 1977. Towards a theory of domination in graphs. Networks 7,247 -261.
  6. Cockayne, E.J. Dreyer, P.A., Hedetniemi, S.M., and Hedetniemi, S.T. 2004. Roman domination in graphs, Discrete math., 278, 11 -22.
  7. Cockayne, E. J., Dawes, R.M., Hedetniemi, S.T. 1980. Total domination in graphs, Networks, 10, 211-219.
  8. Hossein Abdollahzadeh Ahangar, Michal A. Henning, Vladimir Samodivkin, Ismael G Yero 2016. Total Roman domination in graphs, Appl. Anal. Discrete math. 10,501-517.
  9. Henning, M.A., Yeo A. 2013. Total domination in graphs.(Springer Mono graphs in Mathematics) ISBN:978-1-4614-6524-9 (Print) 978-1-4614-6525-6(Online).
  10. Ian Stewart. 1999. Defend the Roman Empire!., Scientific American, 281(6), 136 -139.
  11. Jaya Subba Reddy. C., Reddappa, M., and Maheswari. B. 2019. Roman domination in a certain type of interval graph, International Journal of Research and analyticalReviews, 6(1), 665–672.
  12. Ore, O. 1962. Theory of Graphs, Amer, Math.Soc. Collaq.Publ.38, Providence.
  13. ReValle, C.S., and Rosing K,E. 2000. Defendens imperium romanum: a classical problem in military Strategy, Amer. Math. Monthly, 107 (7), 585 -594.

Keywords

Total domination number, Total Roman dominating function, Total Roman domination number, Interval family, Interval graph