Roman Domination In An Interval Graph With Adjacent Cliques Of Size 3

M. Reddappa; C. Jaya Subba Reddy; B. Maheswari

doi:https://doi.org/10.14445/22315373/IJMTT-V65I9P516

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 9 | Year 2019 | Article Id. IJMTT-V65I9P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I9P516

Roman Domination In An Interval Graph With Adjacent Cliques Of Size 3

M. Reddappa , C. Jaya Subba Reddy , B. Maheswari

Citation :

M. Reddappa , C. Jaya Subba Reddy , B. Maheswari, "Roman Domination In An Interval Graph With Adjacent Cliques Of Size 3," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 9, pp. 107-115, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I9P516

Abstract

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 modelling problems arising in the real world. The theory of domination in graphs introduced by Ore [1] and Berge [7] 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. [2], [3]. A Roman dominating function on a graph G(V,E) is a function f:V->{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 a Roman dominating function is the value f(v) =Σ vev f(v) The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this paper a study of Roman domination and Roman domination number of a certain type of Interval graph is carried out.

Keywords

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

References

[1] O.Ore, “Theory of Graphs”, Amer, Math.Soc. Collaq.Publ.38, Providence 1962.
[2] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, “Domination in graphs: Advanced Topics”, Marcel Dekkar, Inc., New York, 1998.
[3] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, “Fundamentals of domination in graphs”, vol.208 of Monographs and Text books in Pure and Applied Mathematics, Marcel Dekkar, New York, 1998.
[4] Ian Stewart, “Defend the Roman Empire!”., Scientific American, vol.281(6), pp.136 -139, 1999.
[5] E.J. Cockayne, and S.T. Hedetniemi, “Towards a theory of domination in graphs”, Networks, vol.7, pp. 247 -261, 1977.
[6] R.B. Allan, and R.C. Laskar, “On domination, Independent domination numbers of a graph”, Discrete Math., vol.23, pp.73-76, 1978.
[7] C. Berge, “Graphs and Hyperactive graphs”, North Holland, Amsterdam in graphs, Networks, vol.10, pp.211 – 215, 1980 .
[8] C.S. ReValle, and K,E. Rosing, “Defendens imperium romanum: a classical problem in military Strategy”, Amer. Math. Monthly, vol. 107 (7), pp. 585 -594, 2000.
[9] E.J. Cockayne, P.A Dreyer, S.M. Hedetniemi, and S.T. Hedetniemi, “ Roman domination in graphs”, Discrete math.,vol.278, pp.11 - 22, 2004.
[10] C .Jaya Subba Reddy, M. Reddappa and B. Maheswari, “Roman domination in a certain type of interval graph”,International Journal of Research and analyticaL Reviews, vol.6, Issue 1, pp. 665–672, February 2019.