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

Topological Integer Additive Set-Graceful Graphs

by N.K. Sudev, K. P. Chithra, K.A. Germina
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 123 - Number 2
Year of Publication: 2015
Authors: N.K. Sudev, K. P. Chithra, K.A. Germina
10.5120/ijca2015905237

N.K. Sudev, K. P. Chithra, K.A. Germina . Topological Integer Additive Set-Graceful Graphs. International Journal of Computer Applications. 123, 2 ( August 2015), 1-4. DOI=10.5120/ijca2015905237

@article{ 10.5120/ijca2015905237,
author = { N.K. Sudev, K. P. Chithra, K.A. Germina },
title = { Topological Integer Additive Set-Graceful Graphs },
journal = { International Journal of Computer Applications },
issue_date = { August 2015 },
volume = { 123 },
number = { 2 },
month = { August },
year = { 2015 },
issn = { 0975-8887 },
pages = { 1-4 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume123/number2/21928-2015905237/ },
doi = { 10.5120/ijca2015905237 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:11:35.324360+05:30
%A N.K. Sudev
%A K. P. Chithra
%A K.A. Germina
%T Topological Integer Additive Set-Graceful Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 123
%N 2
%P 1-4
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Let N0 denote the set of all non-negative integers and X be any subset of X. Also denote the power set of X by P(X). An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) ! P(X) such that the induced function f+ : E(G) ! P(X) is defined by f+(uv) = f(u) + f(v), where f(u) + f(v) is the sumset of f(u) and f(v). An IASL f is said to be a topological IASL (Top-IASL) if f(V (G)) [ f;g is a topology of the ground set X. An IASL is said to be an integer additive set-graceful labeling (IASGL) if for the induced edgefunction f+, f+(E(G)) = P(X)??f;; f0gg. In this paper, we study certain types of IASL of a given graph G, which is a topological integer additive set-labeling as well as an integer additive set-graceful labeling of G.

References
  1. B. D. Acharya, Set-Valuations and Their Applications, MRI Lecture notes in Applied Mathematics, No.2, The Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad, 1983.
  2. B. D. Acharya, Set-Indexers of a Graph and Set-Graceful Graphs, Bulletin of Allahabad Mathematical Society, 16(2001), 1-23.
  3. B. D. Acharya, K. A. Germina, K. L. Princy and S. B. Rao, Topologically Set-Graceful Graphs, Journal of Combinatorics, Information and System Sciences, 37(2-4)(2012), 299-318.
  4. J. A. Bondy and U. S. R. Murty, Graph theory with applications, Macmillan Press, London, 1976.
  5. A. Brandst¨adt, V. B. Le and J. P. Spinrad, Graph Classes: A Survey, SIAM, Philadelphia, 1987.
  6. J. A. Gallian, A Dynamic Survey of Graph Labelling, The Electronic Journal of Combinatorics, DS-6, 2013.
  7. K. A. Germina and T. M. K. Anandavally, Integer Additive Set-Indexers of a Graph:Sum Square Graphs, Journal of Combinatorics, Information and System Sciences, 37(2-4)(2012), 345-358.
  8. K. A. Germina and N. K. Sudev, On Weakly Uniform Integer Additive Set-Indexers of Graphs, International Mathematical Forum, 8(37)(2013), 1827-1834. DOI: 10.12988/imf.2013.310188.
  9. K. D. Joshy, Introduction to General Topology, New Age International, New Delhi, 1983.
  10. V. Krishnamoorthy, On the Number of Topologies of Finite Sets, The Amer. Math. Monthly, 73(2)(1966), 154-157.
  11. F. Harary, Graph Theory, Addison-Wesley Publishing Company Inc., Philippines, 1969.
  12. W. Imrich, S. Klavzar, Product Graphs: Structure and Recognition, Wiley, 2000.
  13. K. D. Joshi, Applied Discrete Structures, New Age International, New Delhi, 2003.
  14. J. R. Munkers, Topology, Prentice Hall, Vol.2., 2000.
  15. A. Rosa, On Certain Valuation of the Vertices of a Graph, in Theory of Graphs, Gordon and Breach, 1967, 349-355.
  16. N. K. Sudev and K. A. Germina, On Integer Additive Set-Indexers of Graphs, International Journal of Matematical Sciences & Engineering Applications, 8(2)(2014),11-22.
  17. N. K. Sudev and K. A. Germina, Some New Results on Strong Integer Additive Set-Indexers of Graphs, Discrete Mathematics, Algorithms & Applications, 7(1)(2015),1-11., DOI: DOI:10.1142/S1793830914500657.
  18. N. K. Sudev, K. A. Germina and K. P. Chithra, A Creative Review on Integer Additive Set-Labeled Graphs, Asian-European Journal of Mathematics, to appear., DOI:10.1142/S1793557115500527.
  19. N. K. Sudev and K. A. Germina, The exquisite Integer Additive Set-Labeling of Graphs, International Journal of Science and Research, 4(3)(2015), 2858-2862.
  20. N. K. Sudev and K. A. Germina, A Study on Topological Integer Additive Set-Labeling of Graphs, Electronic Journal of Graph Theory and Applications, 3(1)(2015), 70-84.DOI:10.5614/ejgta.2015.3.1.8.
  21. N. K. Sudev and K. A. Germina, A Study on Integer Additive Set-Graceful Graphs, Journal of Pure and Applied Mathematics, to appear.
  22. D. B. West, Introduction to Graph Theory, Pearson Education Inc., 2001.
Index Terms

Computer Science
Information Sciences

Keywords

Integer additive set-labeled graphs integer additive set-graceful graphs topological integer additive set-labeled graph topological integer additive set-graceful labeling of graphs

Powered by PhDFocusTM