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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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IEEE Style Citation: D.K. Thakkar, S.M. Badiyani, “Independent Roman Domination Number of Graphs,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.2, pp.29-34, 2018.

MLA Style Citation: D.K. Thakkar, S.M. Badiyani "Independent Roman Domination Number of Graphs." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.2 (2018): 29-34.

APA Style Citation: D.K. Thakkar, S.M. Badiyani, (2018). Independent Roman Domination Number of Graphs. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(2), 29-34.

BibTex Style Citation:
@article{Thakkar_2018,
author = {D.K. Thakkar, S.M. Badiyani},
title = {Independent Roman Domination Number of Graphs},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {4 2018},
volume = {5},
Issue = {2},
month = {4},
year = {2018},
issn = {2347-2693},
pages = {29-34},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=575},
doi = {https://doi.org/10.26438/ijcse/v5i2.2934}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i2.2934}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=575
TI - Independent Roman Domination Number of Graphs
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - D.K. Thakkar, S.M. Badiyani
PY - 2018
DA - 2018/04/30
PB - IJCSE, Indore, INDIA
SP - 29-34
IS - 2
VL - 5
SN - 2347-2693
ER -

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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.

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