CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Some Domination Parameters of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs

by S. Uma Maheswari, B. Maheswari, M. Manjuri
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 58 - Number 9
Year of Publication: 2012
Authors: S. Uma Maheswari, B. Maheswari, M. Manjuri
10.5120/9312-3544

S. Uma Maheswari, B. Maheswari, M. Manjuri . Some Domination Parameters of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs. International Journal of Computer Applications. 58, 9 ( November 2012), 32-38. DOI=10.5120/9312-3544

@article{ 10.5120/9312-3544,
author = { S. Uma Maheswari, B. Maheswari, M. Manjuri },
title = { Some Domination Parameters of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs },
journal = { International Journal of Computer Applications },
issue_date = { November 2012 },
volume = { 58 },
number = { 9 },
month = { November },
year = { 2012 },
issn = { 0975-8887 },
pages = { 32-38 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume58/number9/9312-3544/ },
doi = { 10.5120/9312-3544 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:02:01.576733+05:30
%A S. Uma Maheswari
%A B. Maheswari
%A M. Manjuri
%T Some Domination Parameters of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 58
%N 9
%P 32-38
%D 2012
%I Foundation of Computer Science (FCS), NY, 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 [1] paved the way for the emergence of a new class of graphs, namely Arithmetic Graphs by introducing the concepts of Number Theory, particularly, the Theory of Congruences in Graph 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. Inspired by the interplay between Number Theory and Graph Theory several researchers in recent times are carrying out extensive studies on various Arithmetic graphs in which adjacency between vertices is defined through various arithmetic functions. In this paper, we consider direct product graphs of Cayley graphs with Arithmetic graphs and present some domination parameters of these graphs.

References
  1. Nathanson and Melvyn B . Connected components of arithmetic graphs, Monat. fur. Math, 29, 219 – 220(1980).
  2. Cockayne, C. J. , Dawes, R. M. and Hedetniemi,S. T. Total domination in graphs, Networks, 10, 211-219 (1980).
  3. Cockayne, E. J. and Hedetniemi, S. T. Towards a theory of domination in graphs, Networks, 7, 247 – 261 (1977).
  4. Whitehead, A. N. and Russel, B. Principia Mathematica, Volume 2, Cambridge University, Press, Cambridge (1912).
  5. Weichsel, P. M. The Kronecker product of graphs, Proc. Amer. Math. Soc. , 13, 47-52, (1962).
  6. Imrich, W. Factoring cardinal product graphs in polynomial time, Discrete Math. , 192, 119-144(1998).
  7. Hammack, R, Imrich, W and Klavzar, S. Handbook of product graphs, CRC Press, (2011).
  8. S. Uma Maheswari, 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).
  9. Madhavi, L. Studies on domination parameters and enumeration of cycle in some Arithmetic graphs, Ph. D. Thesis submitted to S. V. University, Tirupati, India, (2002).
  10. S. Uma Maheswari and B. Maheswari, Domination parameters of Euler Totient Cayley graphs, Rev. Bull. Cal. Math. Soc. , 19,(2),207-214(2011).
  11. Vasumathi, N. Number theoretic graphs, Ph. D. Thesis submitted to S. V. University, Tirupati, India, (1994).
  12. S. Uma Maheswari and B. Maheswari, Some domination parameters of Arithmetic graph V_n, IOSRJM, 2,(6), 14- 18 (2012).
  13. S. Uma Maheswari and B. Maheswari, Some properties of direct product graphs of Cayley graphs with Arithmetic graphs, 54, (14), 34-37,(2012).
Index Terms

Computer Science
Information Sciences

Keywords

Dominating set Total Dominating set Euler Totient Cayley Graph Arithmetic V_n graph Direct Product Graph

Powered by PhDFocusTM