CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
SFLA-Based Line Balancing and Task Optimization in Master-Slave Controlled Hanger Transportation Systems for Garment Production

Duc Hoang Nguyen
Random Articles
Reseach Article

Total Domination Number and Chromatic Number of a Fuzzy Graph

by S. Vimala, J. S. Sathya
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 52 - Number 3
Year of Publication: 2012
Authors: S. Vimala, J. S. Sathya
10.5120/8180-1505

S. Vimala, J. S. Sathya . Total Domination Number and Chromatic Number of a Fuzzy Graph. International Journal of Computer Applications. 52, 3 ( August 2012), 6-10. DOI=10.5120/8180-1505

@article{ 10.5120/8180-1505,
author = { S. Vimala, J. S. Sathya },
title = { Total Domination Number and Chromatic Number of a Fuzzy Graph },
journal = { International Journal of Computer Applications },
issue_date = { August 2012 },
volume = { 52 },
number = { 3 },
month = { August },
year = { 2012 },
issn = { 0975-8887 },
pages = { 6-10 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume52/number3/8180-1505/ },
doi = { 10.5120/8180-1505 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:51:18.840826+05:30
%A S. Vimala
%A J. S. Sathya
%T Total Domination Number and Chromatic Number of a Fuzzy Graph
%J International Journal of Computer Applications
%@ 0975-8887
%V 52
%N 3
%P 6-10
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A subset S of V is called a domination set in G if every vertex in V-S is adjacent to at least one vertex in S. A dominating set is said to be Fuzzy Total Dominating set if every vertex in V is adjacent to at least one vertex in S. Minimum cardinality taken over all total dominating set is called as fuzzy total domination number and is denoted by ?_(ft )(G). The minimum number of colours required to colour all the vertices such that adjacent vertices do not receive the same colour is the chromatic number ?(G). For any graph G a complete sub graph of G is called a clique of G. In this paper we find an upper bound for the sum of the fuzzy total domination and chromatic number in fuzzy graphs and characterize the corresponding extremal fuzzy graphs.

References
  1. Teresa W. Haynes, Stephen T. Hedemiemi and Peter J. Slater (1998), fundamentals of Domination in graphs, Marcel Dekker, Newyork.
  2. Hanary F and Teresa W. Haynes,(2000), Double Domination in graphs, ARC Combinatoria 55, pp. 201-213
  3. Haynes, Teresa W. (2001): Paired domination in Graphs, Congr. Number 150
  4. Mahadevan G, Selvam A, (2008): On independent domination number and chromatic number of a graph, Acta Ciencia Indica, preprint
  5. Paulraj Joseph J. and Arumugam S. (1992): Domination and connectivity in graphs, International Journal of Management and systems, 8 No. 3: 233-236.
  6. Kaufmann. A. , (1975), Introduction to the theory of Fuzzy Subsets, Academic Press, Newyork.
  7. Rosenfield,A. , Fuzzy graphs In: Zadeh, L. A. , Fu, K. S. , Shimura, M. (Eds), Fuzzy sets and their applications(Academic Press, New York)
  8. Somasundaram. A, Somasundaram,S. 1998, Domination in Fuzzy Graphs – I, Pattern Recognition Letters, 19, pp-787-791.
  9. Somasundaram. A, (2004), Domination in Fuzzy Graphs – II, Journal of Fuzzy Mathematics, 20.
  10. Somasundaram. A, (2005), Domination in Product of Fuzzy Graphs, "International Journal of Uncertainity" , Fuzziness and Knowledge-Based Syatems, 13(2), pp. 195-205.
  11. Zadeh,L. A. (1971), Similarity Relations and Fuzzy Ordering, Information sciences, 3(2),pp. 177-200.
  12. Mahadevan G,(2005): On domination theory and related concepts in graphs, Ph. D. thesis, Manonmaniam Sundaranar University,Tirunelveli,India.
  13. Paulraj Joseph J. and Arumugam S. (1997): Domination and colouring in graphs. International Journal of Management and Systems, Vol. 8 No. 1, 37-44.
  14. Paulraj Joseph J, Mahadevan G, Selvam A (2004). On Complementary Perfect domination number of a graph, Acta Ciencia India, vol. XXXIM, No. 2,847(2006).
  15. Vimala S, Sathya J. S, "Graphs whose sum of Chromatic number and Total domination equals to 2n-5 for any n>4", Proceedings of the Heber International Conference on Applications of Mathematics and statistics, Tiruchirappalli pp 375-381
  16. Tamizh Chelvam T and Jaya Prasad B. (2004): On independent domination number, Referred Proceedings of the National conference on Graph theory and its applications, conducted by Anna University, edited by R. Balakrishnan. Prof Wilson, and G. Setheraman, 108-111, Narosa publishing House, New Delhi, India pp. 108-111
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy Total Domination Number Chromatic Number Clique Fuzzy Graphs

Powered by PhDFocusTM