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Signed And Roman Edge Dominating Functions Of Corona Product Graph Of A Cycle With A Complete Graph

J. Anitha B. Maheswari

Subject area: Science,Engineering and Technology  ·  Area of research: Mathematics

Abstract

Graph Theory has been realized as one of the most useful branches of Mathematics of recent origin with wide applications to combinatorial problems and classical algebraic problems. Graph theory has applications in diverse areas such as social sciences, linguistics, physical sciences, communication engineering etc. 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. 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 [13, 14]. Frucht and Harary [11] introduced a new product on two graphs G1 and G2, called corona product denoted by G18G2. The object is to construct a new and simple operation on two graphs G1 and G2 called their corona, with the property that the group of the new graph is in general isomorphic with the wreath product of the groups of G1 and of G2. In this paper, some results on minimal signed and Roman edge dominating functions of corona product graph of a cycle with a complete graph are presented.

Keywords

Corona Product, Cycle, Complete graph, Signed edge dominating function, Roman edge dominating function

References

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[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, December (2016), pp.151-160.

[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, January (2017), pp. 40-44.

[4] Anitha, J. and Maheswari, B. - Total Edge Dominating sets and functions of Corona Product Graph of a Cycle with a Complete Graph – Asia Mathematika (Communicated).

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

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

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

[9] 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, 1995, pp. 311 – 321.

[10] R. Dutton and W. F. Klostermeyer - Edge dominating sets and vertex covers, Discussions Mathematicae, vol. 33, no.2, 2013, pp.437-456.

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

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

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

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

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

[16] Jayaram, S. R. - Line domination in graphs, Graphs and Combinatorics, vol. 3, no. 4, 1987, pp. 357–363.

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

[18] Mitchell S, Hedetniemi, S.T. - Edge domination in trees. Congr. Numer., 19 , 1977 , pp.489-509.

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

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How to cite this paper

J. Anitha, B. Maheswari "Signed And Roman Edge Dominating Functions Of Corona Product Graph Of A Cycle With A Complete Graph" Iconic Research And Engineering Journals Volume 3 Issue 2 2019 Page 677-683
J. Anitha, B. Maheswari "Signed And Roman Edge Dominating Functions Of Corona Product Graph Of A Cycle With A Complete Graph" Iconic Research And Engineering Journals, vol. 3, no. 2, Aug. 2019
J. Anitha, B. Maheswari (2019). Signed And Roman Edge Dominating Functions Of Corona Product Graph Of A Cycle With A Complete Graph. Iconic Research And Engineering Journals, 3(2).
J. Anitha, B. Maheswari "Signed And Roman Edge Dominating Functions Of Corona Product Graph Of A Cycle With A Complete Graph" Iconic Research And Engineering Journals, vol. 3, no. 2, Aug. 2019.
@article{1701575,
      author = {J. Anitha, B. Maheswari},
      title = {Signed And Roman Edge Dominating Functions Of Corona Product Graph Of A Cycle With A Complete Graph},
      journal = {Iconic Research And Engineering Journals},
      year = {2019},
      volume = {3},
      number = {2},
      pages = {677-683},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1701575.pdf},
      abstract = {Graph Theory has been realized as one of the most useful branches of Mathematics of recent origin with wide applications to combinatorial problems and classical algebraic problems. Graph theory has applications in diverse areas such as social sciences, linguistics, physical sciences, communication engineering etc. 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. 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 [13, 14]. Frucht and Harary [11] introduced a new product on two graphs G1 and G2, called corona product denoted by G18G2. The object is to construct a new and simple operation on two graphs G1 and G2 called their corona, with the property that the group of the new graph is in general isomorphic with the wreath product of the groups of G1 and of G2. In this paper, some results on minimal signed and Roman edge dominating functions of corona product graph of a cycle with a complete graph are presented.},
      keywords = {Corona Product, Cycle, Complete graph, Signed edge dominating function, Roman edge dominating function},
      month = {August},
  }