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Strong Dominating Sets of Lexicographic Product Graph of Cayley Graphs with Arithmetic Graphs

M. Manjuri, B. Maheswari Published in Applied Mathematics

International Journal of Applied Information Systems
Year of Publication: 2013
© 2013 by IJAIS Journal
10.5120/ijais13-451065
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  1. M Manjuri and B Maheswari. Article: Strong Dominating Sets of Lexicographic Product Graph of Cayley Graphs with Arithmetic Graphs. International Journal of Applied Information Systems 6(6):25-29, December 2013. BibTeX

    @article{key:article,
    	author = "M. Manjuri and B. Maheswari",
    	title = "Article: Strong Dominating Sets of Lexicographic Product Graph of Cayley Graphs with Arithmetic Graphs",
    	journal = "International Journal of Applied Information Systems",
    	year = 2013,
    	volume = 6,
    	number = 6,
    	pages = "25-29",
    	month = "December",
    	note = "Published by Foundation of Computer Science, New York, USA"
    }
    

Abstract

Number Theory is one of the oldest branches of mathematics, which inherited rich contributions from almost all greatest mathematicians, ancient and modern. Nathanson [7] paved the way for the emergence of a new class of graphs, namely Arithmetic Graphs by introducing the concepts of Number Theory. Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley graph becomes an Arithmetic graph. Product of graphs are introduced in Graph Theory very recently and developing rapidly. In this paper, we consider lexicographic product graphs of Cayley graphs with Arithmetic graphs and present strong domination parameter of these graphs.

Reference

  1. Feigenbaum, J. and Schaffer, A. A. - Recognizing composite graphs is equivalent to testing graph isomorphism, SIAM-J. Comput. , 15 (1986), 619-627.
  2. Geller, D. and Stahl, S. - The chromatic number and other functions of the lexicographic product, J. Combin. Theory Ser. B, 19 (1975), 87-95.
  3. Harary, F. - On the group of the composition of two graphs, Duke Math. J. , 26 (1959), 29-36.
  4. Imrich, W. and Klavzar, S. -Product graphs: Structure and recognition, John Wiley & Sons, New York, USA(2000).
  5. Madhavi, L. - Studies on domination parameters and enumeration of cycles in some Arithmetic graphs, Ph. D. Thesis submitted to S. V. University, Tirupati, India, (2002).
  6. Manjuri,M. and Maheswari,B. - Strong dominating sets of Euler totient Cayley graph and Arithmetic Vn graphs, IJCA (Communicated).
  7. Nathanson and Melvyn B. - Connected components of arithmetic graphs, Monat. fur. Math, 29 (1980), 219 – 220.
  8. Sampathkumar, E. and Pushpa Latha, L. -Strong weak domination and domination balance in graph, Discrete Mathematics, 161 (1996), 235-242.
  9. Uma Maheswari, S. - Some studies on the product graphs of Euler Totient Cayley graphs and Arithmetic V_n graphs, Ph. D. Thesis submitted to S. P. Women's University, Tirupati, India, (2012).

Keywords

Euler Totient Cayley graph, Arithmetic V_n graph, lexicographic product graph, strong domination.