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

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Convexity of Minimal Dominating and Total Dominating Functions of Corona Product Graph of a Cycle with a Complete Graph

by M. Siva Parvathi, B. Maheswari
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 88 - Number 5
Year of Publication: 2014
Authors: M. Siva Parvathi, B. Maheswari
10.5120/15346-3687

M. Siva Parvathi, B. Maheswari . Convexity of Minimal Dominating and Total Dominating Functions of Corona Product Graph of a Cycle with a Complete Graph. International Journal of Computer Applications. 88, 5 ( February 2014), 5-8. DOI=10.5120/15346-3687

@article{ 10.5120/15346-3687,
author = { M. Siva Parvathi, B. Maheswari },
title = { Convexity of Minimal Dominating and Total Dominating Functions of Corona Product Graph of a Cycle with a Complete Graph },
journal = { International Journal of Computer Applications },
issue_date = { February 2014 },
volume = { 88 },
number = { 5 },
month = { February },
year = { 2014 },
issn = { 0975-8887 },
pages = { 5-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume88/number5/15346-3687/ },
doi = { 10.5120/15346-3687 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:07:19.853813+05:30
%A M. Siva Parvathi
%A B. Maheswari
%T Convexity of Minimal Dominating and Total Dominating Functions of Corona Product Graph of a Cycle with a Complete Graph
%J International Journal of Computer Applications
%@ 0975-8887
%V 88
%N 5
%P 5-8
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

'Domination in graphs' has been studied extensively and at present it is an emerging area of research in graph theory. 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]. Product of graphs occurs naturally in discrete mathematics as tools in combinatorial constructions. They give rise to an important classes of graphs and deep structural problems. In this paper we study the dominating and total dominating functions of corona product graph of a cycle with a complete graph.

References
  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), 73 – 76.
  4. Cockayne, E. J. and Hedetniemi, S. T. - Towards a theory of domination in graphs. Networks, 7 (1977), 247 – 261.
  5. Cockayne, C. J. , Dawes, R. M. and Hedetniemi, S. T Total domination in graphs, Networks, 10 (1980), 211 – 219.
  6. Jeelani Begum, S. - Some studies on dominating functions of Quadratic Residue Cayley Graphs, Ph. D. thesis, Sri Padmavathi Mahila Visvavidyalayam,Tirupati, Andhra Pradesh, India, (2011).
  7. Frucht, R. and Harary, F. - On the corona of Two Graphs, Aequationes Mathematicae, Volume 4, Issue 3 (1970), 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), 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), 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 Science and Technology (accepted).
  12. Cockayne, E. J. , Mynhardt, C. M. and Yu, B. Total dominating functions in trees: Minimality and Convexity, Journal of Graph Theory, 19(1995), 83 – 92.
  13. Yu, B. , Convexity of minimal total dominating functions in graphs, J. Graph Theory, 24 (4) (1997), 313 – 321.
  14. Reji Kumar, K. , Studies in Graph Theory – Dominating functions, Ph. D. thesis, Manonmaniam Sundaranar University, Tirunelveli, India, (2004).
  15. Cockayne, E. J. and Mynhardt, C. M. Convexity of extremal domination – related functions of graphs. In: Domination in Graphs – Advaned Topics, (Ed. T. W. Haynes, S. T. Hedetniemi, P. J. Slater), Marcel Dekker, New York, (1998), 109 – 131.
  16. 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).
Index Terms

Computer Science
Information Sciences

Keywords

Corona Product Cycle Complete Graph Dominating function Total dominating function.

Powered by PhDFocusTM