Call for Paper - January 2023 Edition
IJCA solicits original research papers for the January 2023 Edition. Last date of manuscript submission is December 20, 2022. Read More

Edge Domination Number of Corona Product Graph of a Cycle with a Star

Print
PDF
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Authors:
J. Sreedevi, B. Maheswari
10.5120/ijca2017912792

J Sreedevi and B Maheswari. Edge Domination Number of Corona Product Graph of a Cycle with a Star. International Journal of Computer Applications 157(8):34-36, January 2017. BibTeX

@article{10.5120/ijca2017912792,
	author = {J. Sreedevi and B. Maheswari},
	title = {Edge Domination Number of Corona Product Graph of a Cycle with a Star},
	journal = {International Journal of Computer Applications},
	issue_date = {January 2017},
	volume = {157},
	number = {8},
	month = {Jan},
	year = {2017},
	issn = {0975-8887},
	pages = {34-36},
	numpages = {3},
	url = {http://www.ijcaonline.org/archives/volume157/number8/26854-2017912792},
	doi = {10.5120/ijca2017912792},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

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 to 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 [7, 8].

Products are often viewed as a convenient language with which one can describe structures, but they are increasingly being applied in more substantial ways. Every branch of mathematics employs some notion of product that enables the combination or decomposition of its elemental structures.

In this paper some results on minimal edge dominating sets of corona product graph of cycle with a star are discussed.

References

  1. .Allan, R.B. and Laskar, R.C. – On domination,  independent domination numbers of a graph, Discrete Math., 23, (1978), pp.73 – 76.
  2. . Arumugam S., Sithara Jerry - Fractional edge domination in graphs, Appl. Anal. Discrete math.3 (2009), pp.359-370.
  3. . Arumugam S., Velammal S - Edge domination in graphs, Taiwanese Journal of Mathematics, 2 (2) (1998), pp.173-179.
  4. . Cockayne, E.J. and Hedetniemi, S.T. - Towards a theory   of domination in graphs, Networks, 7, (1977), pp.247 – 261.
  5. . R. Dutton and W. F. Klostermeyer - Edge dominating sets and vertex covers, Discussions Mathematicae, vol. 33, no.2, (2013), pp.437-456.
  6. . Frucht, R. and Harary, F. - On the corona of Two Graphs, Aequationes Mathematicae, Volume 4, Issue 3, (1970), pp.322 – 325.
  7. .Haynes, T.W., Hedetniemi, S.T.  and  Slater, P.J.  - Domination in Graphs: Advanced Topics, Marcel Dekker, Inc., New York, (1998).
  8. . Haynes, T.W., Hedetniemi, S.T. and Slater, P.J. - Fundamentals of domination in graphs, Marcel Dekker, Inc., New York , (1998).
  9. . Jayaram, S. R - Line domination in graphs, Graphs and Combinatorics, vol. 3, no. 4, (1987), pp. 357–363.
  10. . 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.
  11. . Mitchell S, Hedetniemi, S.T. - Edge domination in trees. Congr. Numer., 19 (1977), pp.489-509.
  12. .Yannakakis, M., Gavril, F. - Edge dominating sets in graphs, SIAM Journal on Applied Mathematics, vol. 38, no. 3, (1980), pp. 364–372.
  13. . Zelinka, B. - Edge domination in graphs of cubes, Czechoslovak Mathematical Journal, vol. 52, no. 4, (2002), pp. 875–879.

Keywords

Corona Product, edge dominating set, edge domination number.