Independent Roman Domination Number of Graphs

D.K. Thakkar¹ , S.M. Badiyani²

1. Department of Mathematics, Saurashtra University Campus, Rajkot, India.
2. Department of Mathematics, Saurashtra University Campus, Rajkot, India.

Correspondence should be addressed to: sankycolors@gmail.com.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.2 , pp.29-34, Apr-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.2934

Online published on Apr 30, 2018

Copyright © D.K. Thakkar, S.M. Badiyani . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this manuscript we consider Independent Roman Dominating Functions for graphs. We characterize minimal Independent Roman Dominating Functions. We observed the change in the Independent Roman Domination Number of a graph when a vertex is removed from the graph. We prove a necessary and sufficient condition under which the Independent Roman Domination Number of a graph increases or decreases. We have defined a new class of graphs called Independent Roman graphs. A necessary and sufficient condition is given under which a graph is an Independent Roman graph.

Key-Words / Index Term :
Independent Roman Dominating Function, Independent Roman Domination Number, minimal Independent Roman Dominating Function, minimum Independent Roman Dominating Function, Independent Roman graph.

References :
[1] C.S.Revelle, K.E.Rosing, “Defenders Imperium Romanum: a classical problem in military strategy”, Amer.Math.Monthly Vol. 107 (7), pp. 585-594, 2000.
[2] D.K.Thakkar and S.M.Badiyani, “MINIMAL ROMAN DOMINATING FUNCTIONS”, International Journal of Mathematics and Soft Computing, Vol. 7, No. 2, pp. 63-71, 2017.
[3] D.K.Thakkar and S.M.Badiyani, “On the Roman Domination Number of Graphs”, International Journal of Mathematical Archive, Vol. 8 (2), pp. 184-188, 2017.
[4] E.J. Cockayne, P.M. Dreyer Jr., S.M Hedetniemi and S.T. Hedetniemi, “On Roman Domination In graphs”, Discrete Math. Vol, 278, pp. 11-22, 2004.
[5] I. Stewart, “Defend the Roman Empire!” Sci. Amer. Vol. 281(6), pp. 136-139, 1999.
[6] M. Adabi, E. E. Targhi, N. J. Rad and M.S. Moradi, “Properties ofIndependent Roman Dominatinon in graphs”, Australasian Journal of Combinatorics, Vol. 52, pp. 11-18, 2012.
[7] N. J. Rad and Lutz Volkmann “Roman Domination Perfect graphs”, An. St. Univ. Ovidius Constanta, Vol. 19 (3), pp. 167-174, 2011.
[8] P. A. Dreyer, Jr. Dissertation Director: Fred S Roberts, “Application and Variations of domination in graphs”, New Brunswick, New Jersey, October 2000.
[9] T.W.Haynes, S.T.Hedetniemi, P.J.Slater, “Fundamental of Domination In graphs”, Marcel Dekker, New York, 1998.
[10] T.W.Haynes, S.T.Hedetniemi, P.J.Slater, “Domination In graphs Advanced Topics”, New York, 1998.