Volume 65 | Issue 8 | Year 2019 | Article Id. IJMTT-V65I8P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I8P518

The theory of Graphs is one of the major areas of combinatorics that has developed into an important branch of Mathematics. The theory of domination in graphs is an emerging area of research in graph theory today. It has been studied extensively and finds applications to various branches of Science & Technology. Frucht and Harary [13] introduced a new product on two graphs G1 and G2, called corona product denoted by G1 . G2 . In this paper, some results on total Signed and Roman edge dominating functions of corona product graph of a cycle with a complete graph are discussed.

[1] Allan, R.B. and Laskar, R.C.– On domination, independent domination numbers of a graph, Discrete Math.23, pp.73 –76 ,1978.

[2] Anitha, J and Maheswari, B. - Edge Dominating functions of Corona Product Graph of a Cycle with a Complete Graph- Open journal of Applied and Theoretical Mathematics (OJATM), Volume.2, No-4, pp.151-160, December , 2016.

[3] Anitha, J. and Maheswari, B. - Edge Dominating number of Corona Product Graph of a Cycle with a Complete Graph- International Journal of Computer Applications (IJCA), Volume 158, No 3, pp. 40-44, January , 2017.

[4] Anitha, J. and Maheswari, B. - Signed and Roman Edge Dominating functions of Corona Product Graph of a Cycle with a Complete Graph – IRE journal (accepted).

[5] Anitha, J. and Maheswari, B.Convexity of Total Y-Edge Domination Variants of Corona Product Graph of a Cycle with a Complete Graph – IJARCSSE (accepted)

[6] Arumugam S., Sithara Jerry. - Fractional edge domination in graphs, Appl. Anal. Discrete math.3, pp.359-370, 2009.

[7] Arumugam S., Velammal S. - Edge domination in graphs, Taiwanese Journal of Mathematics, 2 (2), pp.173-179, 1998.

[8] Berge, C - The Theory of Graphs and its Applications, Methuen, London , 1962.

[9] Cockayne, E.J. and Hedetniemi, S.T. - Towards a theory of domination in graphs, Networks, 7, pp.247 – 261, 1977.

[10] Cockayne, C.J., Dawes, R.M., Hedetniemi, S.T. - Total domination in graphs, Networks, 10, pp. 211 – 219, 1980.

[11] Cockayne, E.J.,Dreyer, P.A., Hedetniemi, S.M. and Hedetniemi, S.T. - Roman domination in graphs, Discrete Math., 278, pp.11 – 22, 2004.

[12] Dunbar.J., Hedetniemi.S.T., Henning, M.A. and Slater, P.J. - Signed domination in graphs, in: Y. Alari and A. Schwenk (Eds.), Proc. 7thInternat. Conf. on the Theory and Applications of Graphs, Wiley, New York , pp. 311 – 321, 1995.

[13] Frucht, R. and Harary, F. - On the corona of Two Graphs, Aequationes Mathematicae, Volume 4, Issue 3, pp.322 – 325, 1970.

[14] Henning, M.A. and Hedetniemi, S.M – Defending the Roman Empire – A new strategy, Discrete Mathematics, 266, pp.239 – 251, 2003.

[15] Haynes, T.W., Hedetniemi, S.T. and Slater, P.J. -Domination in Graphs: Advanced Topics, Marcel Dekker, Inc., New York, 1998.

[16] Haynes, T.W., Hedetniemi, S.T. and Slater, P.J. - Fundamentals of domination in graphs, Marcel Dekker, Inc., New York 1998.

[17] Ian Stewart - Defend the Roman Empire!, Scientific American, 281(6), pp. 136 – 139, 1999.

[18] Kulli, R., Soner, N. D. - Complementary edge domination in graphs, Indian Journal of Pure and Applied Mathematics, vol. 28, no. 7, pp. 917–920, 1997.

[19] Mitchell S, Hedetniemi, S.T. - Edge domination in trees. Congr. Numer., 19 , pp.489-509, 1977. [20] Ore, O. - Theory of Graphs, Amer.Soc.Colloq.Publ.Vol.38. Amer. Math.Soc.,Providence, RI, 1962.

[21] Reji Kumar, K - Studies in Graph Theory – Dominating functions, Ph.D. thesis, Manonmaniam Sundaranar University, Tirunelveli, India, 2004.

[22] ReVelle, C.S. and Rosing, K.E. - Defendens imperium romanum: a classical problem in military strategy, Amer. Math. Monthly, 107 (7), pp.585 – 594, 2000.

[23] Sampath Kumar, E. - Proceedings of a Symposium on Graph Theory and Combinatorics, Kochi, Kerala, India, 17 – 19 ,May, 1991.

[24] Zelinka, B. - Edge domination in graphs of cubes, Czechoslovak Mathematical Journal, vol. 52, no. 4, pp. 875–879, 2002.

[25] Zelinka, B. - Signed total domination number of a graph, Czechoslovak Mathematical Journal, Vol. 51, No.2, pp.225 – 229, 2001.

Anitha .J , Maheswari .B, "Total Signed And Roman Edge
Dominating Functions of Corona Product
Graph of A Cycle With A Complete Graph," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 65, no. 8, pp. 158-165, 2019. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V65I8P518