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Unidominating Functions of Corona Product Graph of a Complete Graph with a Wheel

B. Aruna, B. Maheswari in Applied Mathematics

International Journal of Applied Information Systems
Year of Publication: 2019
Publisher: Foundation of Computer Science (FCS), NY, USA
Authors:B. Aruna, B. Maheswari
10.5120/ijais2019451829
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  1. B Aruna and B Maheswari. Unidominating Functions of Corona Product Graph of a Complete Graph with a Wheel. International Journal of Applied Information Systems 12(26):6-9, December 2019. URL, DOI BibTeX

    @article{10.5120/ijais2019451829,
    	author = "B. Aruna and B. Maheswari",
    	title = "Unidominating Functions of Corona Product Graph of a Complete Graph with a Wheel",
    	journal = "International Journal of Applied Information Systems",
    	issue_date = "December, 2019",
    	volume = 12,
    	number = 26,
    	month = "December",
    	year = 2019,
    	issn = "2249-0868",
    	pages = "6-9",
    	url = "http://www.ijais.org/archives/volume12/number26/1072-2019451829",
    	doi = "10.5120/ijais2019451829",
    	publisher = "Foundation of Computer Science (FCS), NY, USA",
    	address = "New York, USA"
    }
    

Abstract

Graph Theory is the fast growing area of research in Mathematics it has wide applications to several fields - like computer science, social sciences, Science and Technology, etc. Recently, Dominating functions in domination theory playing a key role as they have interesting applications. The theory of domination in graphs introduced by Ore [7] and Berge [2] is an attractive area of research in graph theory in the last three decades.

The concepts of dominating functions are introduced by Hedetniemi [4]. Corona product graphs is a new concept introduced by Frucht and Harary [3] has become an inviting area of research at present. Anantha Lakshmi [1] has introduced new concepts unidomination, upper unidomination, minimal unidominating function of a graph and studied these functions for some standard graphs.

In this paper the authors have studied the concept of unidominating function and upper unidomination number for corona product graph ? K?_n ? W_(1,m) and determined the unidomination number and upper unidomination number for ? K?_n ? W_(1,m). Also the number of unidominating functions of minimum weight is found.

Reference

  1. Anantha Lakshmi, V. A Study on Unidominating and Total Unidominating functions of Some Standard
  2. Graphs, Ph.D. thesis, Sri Padmavati Mahila Visvavidyalayam, Tirupati, Andhra Pradesh, India, (2015).
  3. Berge, C. The Theory of Graphs and its Applications, Methuen, London (1962).
  4. Frucht, R. Harary, F On the corona of Two Graphs. AequationesMathematicae, 1970, Volume 4, Issue 3, pp. 322-325
  5. Hedetniemi S .M, Hedetniemi, S.T. and Wimer, T. V. - Linear time resource allocation algorithms for trees. Technical report URI – 014, Department of Mathematics, Clemson University, 1987.
  6. T.W. Haynes, T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
  7. T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Domination in Graphs: Advanced Topics,Marcel Dekker, New York, 1998.
  8. Ore, O. Theory of Graphs, Amer. Soc. Colloq. Publ. Vol.38. Amer. Math. Soc., Providence, RI, (1962).

Keywords

Unidominating function, unidomination number, minimal unidominating function, upper unidomination number