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Signed Dominating and Total Dominating Functions of Corona Product Graph of a Path with a Star

M. Siva Parvathi, B. Maheswari Published in Applied Mathematics

International Journal of Applied Information Systems
Year of Publication: 2014
© 2013 by IJAIS Journal
10.5120/ijais14-451105
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  1. Siva M Parvathi and B Maheswari. Article: Signed Dominating and Total Dominating Functions of Corona Product Graph of a Path with a Star. International Journal of Applied Information Systems 6(9):36-41, March 2014. BibTeX

    @article{key:article,
    	author = "M. Siva Parvathi and B. Maheswari",
    	title = "Article: Signed Dominating and Total Dominating Functions of Corona Product Graph of a Path with a Star",
    	journal = "International Journal of Applied Information Systems",
    	year = 2014,
    	volume = 6,
    	number = 9,
    	pages = "36-41",
    	month = "March",
    	note = "Published by Foundation of Computer Science, New York, USA"
    }
    

Abstract

Domination in graphs has been an extensively researched branch of graph theory. Graph theory is one of the most flourishing branches of modern mathematics and computer applications. 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. [ 1, 2]. Recently dominating functions in domination theory have received much attention. In this paper we present some results on minimal signed dominating functions and minimal total signed dominating functions of corona product graph of a path with a star.

Reference

  1. Haynes, T. W. , Hedetniemi, S. T. and Slater, P. J. - Domination in Graphs: Advanced Topics, Marcel Dekker Inc. , New York, 1998.
  2. Haynes, T. W. , Hedetniemi, S. T. and Slater, P. J. Fundamentals of domination in graphs, Marcel Dekker Inc. , New York , 1998.
  3. Allan, R. B. and Laskar, R. C. – On domination, independent domination numbers of a graph, Discrete Math. , 23, 1978, pp. 73 – 76.
  4. Cockayne, E. J. and Hedetniemi, S. T. - Towards a theory of domination in graphs. Networks, 7, 1977, pp. 247 – 261.
  5. Dunbar,J. ,Hedetniemi,S. T,Henning,M. A. and Slater,P. J Signed domination in graphs, in: Y. Alari and A. Schwenk(Eds. ), Proc. 7th Internat. Conf. on the Theory and Applications of Graphs, Wiley, New York, 1995, pp. 311 – 321.
  6. Zelinka, B. - Signed total domination number of a graph, Czechoslovak Mathematical Journal, Vol. 51, No. 2, 2001, pp. 225 – 229.
  7. Frucht, R. and Harary, F. - On the corona of Two Graphs, Aequationes Mathematicae, Volume 4, Issue 3, 1970, pp. 322 – 325.
  8. Siva Parvathi, M – Some studies on dominating functions of corona product graphs, Ph. D thesis, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India, 2013.
  9. Siva Parvathi, M and Maheswari, B . - Minimal Dominating Functions of Corona Product Graph of a Cycle with a Complete Graph - International Journal of Computer Engineering & Technology, Volume 4, Issue 4, 2013, pp. 248 – 256.
  10. Siva Parvathi, M and Maheswari, B. - Some variations of Y-Dominating Functions of Corona Product Graph of a Cycle with a Complete Graph - International Journal of Computer Applications, Volume 81, Issue 1, 2013, pp. 16 – 21.
  11. Siva Parvathi, M and Maheswari, B. - Some variations of Total Y-Dominating Functions of Corona Product Graph of a Cycle with a Complete Graph - Fire Journal of Science and Technology (accepted).
  12. Siva Parvathi, M and Maheswari, B. - Minimal total dominating functions of corona product graph of a cycle with a complete graph – International Journal of Applied Information Systems (communicated).
  13. Siva Parvathi, M and Maheswari, B. - Convexity of minimal dominating and total dominating functions of corona product graph of a cycle with a complete graph – International Journal of Computer Applications (communicated).

Keywords

Corona Product, signed dominating function, Total signed dominating function.