### On Pairs of Disjoint Dominating Sets in the Composition of Graphs

#### Abstract

In this paper, we investigate pairs of disjoint dominating sets *A* and *B* in the composition of graph, where *B* is either an independent or a total dominating set in the composition of graph.

#### Full Text:

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R.B. Allan and R. Laskar, On domination and independent domination

numbers of a graph, Discrete Mathematics, Vol.23, No.2, 73-76, 1978.

V. Anusuya, R. Kala, A Note on Disjoint Dominating Sets in Graphs, Int.

J. Contemp. Math. Sciences, Vol. 7, 2012.

C. Berge, Theory of Graphs and its Applications, Methuen, London, 1962.

F. Buckley, F. Harary. Distance in Graphs. Redwood City. CA: Addison

Wesley. 1990.

S.R. Canoy Jr. and M.A. Labendia, Independent domination in graphs

under some binary operations, to appear.

S.R. Canoy Jr. and C.E. Go, Domination in the composition and Cartesian

product of graphs, AKCE, to appear.

E. J. Cockayne, R. M. Dawes, and S. T. Hedetnieme. Total domination

in graphs. Networks, 10(3):211-219, 1980.

E. J. Cockayne and S. T. Hedetniemi, Towards a Theory of Domination

in Graph. Networks 7 (1977) 247-261.

G.S. Domke, J.E. Dunbar, and L.R. Markus, The inverse domination

number of a graph, Ars Combin., 72 (2004), 149-160.

W. Duckworth and N.C. Wormald(2006), On the independent domination

number of random regular graphs, Combinatorics, Probability and

Computing, Vol.15, No.4, pp 513-522.

T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination

in Graphs. Marcel Dekker, Inc. New York(1998).

T. Haynes, S.Hedetniemi and M. Henning, Domination in graphs applied

to electrical power networks, J. Discrete Math. 15(4), 519-529, 2000.

S.M. Hedetniemi, S.T. Hedetniemi, R.C. Laskar, L. Markus, and P.J.

Slater, Disjoint dominating sets in graphs, manuscript 2007.

Hedetniemi T.W., Hedetniemi S.T, Renu C.Laskar, Slater P.J., Disjoint

dominating sets, Proceedings of Int. conf. on Disc. Math.(ICDM 2006)

-102.

M.A. Henning, C. Lowenstein, and D. Rautenbach, Remarks about disjoint

dominating sets, Discrete Mathematics, 309 (2009), no. 23-24, 6451-6458.

http://dx.doi.org/10.1016/j.disc.2009.06.017.

M.A. Henning and J. Southey, A note on graphs with disjoint dominating

and total dominating sets, Ars Combin 89 (2008), 159-162.

M.A. Henning and J. Southey, A characterization of graphs with dis-

joint dominating and total dominating sets, Quaestiones Mathematicae

(2009), 119-129.

M.A. Henning, C. Lowenstein and D. Rautenbach, Partitioning a graph

into a dominating set, a total dominating set, and something else, Discus-

siones Mathematicae: Graph Theory;2010, Vol. 30 Issue 4, p563.

E.M. Kiunisala and F.P. Jamil, Inverse domination numbers and disjoint

domination numbers of graphs under some binary operations, Applied

Mathematical Sciences, Vol. 8, 2014, no. 107, 5303 - 5315.

E.M. Kiunisala and F.P. Jamil, On Pairs of Disjoint Dominating Sets in

a graph, International Journal of Mathematical Analysis, Vol. 10, 2016,

no. 13, 623-637.

V.R. Kulli and S.C. Sigarkanti, Inverse domination in graphs, Nat. Acad.

Sci. Letters, 14 (1991) 473-475.

Kulli V.R.,and Iyer R.R., Inverse total domination in graphs, J.Discrete

Mathematical Sciences and Cryptography, Vol. 10 Number 5 (2007), pp

-620.

C.Lowenstein and D.Rautenbach, Pairs of disjoint Dominating sets and

the minimum degree of graphs, Graphs and Combinatorics, 26 (2010),

-424. http://dx.doi.org/10.1007/s00373-010-0918-9

O. Ore, Theory of graphs, Amer. math. Soc. Transl., 38(Amer. Math. Soc.,

Providence, RI, 1962), 206-212.

H. B. Walikar, B. D. Acharya and E. Sampathkumar, Recent Develop-

ments in the Theory of Domination in Graphs and its Applications. MRI

Lecture Notes in Mathematics 1 (1979).

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