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On the Sparing Number of the Edge-Corona of Graphs

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International Journal of Computer Applications
© 2015 by IJCA Journal
Volume 118 - Number 1
Year of Publication: 2015
Authors:
K. P. Chithra
K. A. Germina
N. K. Sudev
10.5120/20706-3025

K P Chithra, K A Germina and N K Sudev. Article: On the Sparing Number of the Edge-Corona of Graphs. International Journal of Computer Applications 118(1):1-5, May 2015. Full text available. BibTeX

@article{key:article,
	author = {K. P. Chithra and K. A. Germina and N. K. Sudev},
	title = {Article: On the Sparing Number of the Edge-Corona of Graphs},
	journal = {International Journal of Computer Applications},
	year = {2015},
	volume = {118},
	number = {1},
	pages = {1-5},
	month = {May},
	note = {Full text available}
}

Abstract

Let N0 be the set of all non-negative integers and P(N0) be its the power set. An integer additive set-indexer (IASI) of a graph G is an injective function f : V (G) ! P(N0) such that the induced function f+ : E(G) ! P(N0) defined by f+(uv) = f(u) + f(v) is also injective, where f(u) + f(v) is the sum set of f(u) and f(v). An integer additive set-indexer f is said to be a weak integer additive set-indexer (weak IASI) if jf+(uv)j = max(jf(u)j; jf(v)j) 8 uv 2 E(G). The minimum number of singleton set-labeled edges required for the graph G to admit a weak IASI is called the sparing number of the graph. In this paper, we discuss the admissibility of weak IASI by a particular type of graph product called the edge corona of two given graphs and determine the sparing number of the edge corona of certain graphs.

References

  • J. A. Bondy and U. S. R. Murty, Graph Theory, Springer, 2008.
  • K. P. Chithra, K. A. Germina and N. K. Sudev, The Sparing Number of the Cartesian product of Certain Graphs, Communications in Mathematics & Applications, 5(1)(2014), 23-30.
  • K. P. Chithra, K. A. Germina and N. K. Sudev, A Study on the Sparing Number of the Corona of Certain Graphs, Research & Reviews: Discrete Mathematical Structures, 1(2)(2014), 5- 15.
  • R. Frucht and F. Harary, On the Corona of Two Graphs, Aequationes Math. , 4(3)(1970), 322-325.
  • J. A. Gallian, A Dynamic Survey of Graph Labelling, The Electronic Journal of Combinatorics, # DS 16, 2013.
  • 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.
  • K. A. Germina and N K Sudev, On Weakly Uniform Integer Additive Set-Indexers of Graphs, International Mathematical Forum, 8(37)(2013), 1827-1834.
  • R. Hammack,W. Imrich and S. Klavzar, Handbook of Product graphs, CRC Press, 2011.
  • F. Harary, Graph Theory, Addison-Wesley Publishing Company Inc. , 1994.
  • Y. Hu and W. C. Shiu, The spectrum of the edge corona of two graphs, Electronic Journal of Linear Algebra, 20(2010), 586-594.
  • N. K. Sudev and K. A. Germina, A Characterisation of Weak Integer Additive Set-Indexers of Graphs, Journal of Fuzzy Set Valued Analysis, 2014(2014), Article Id: jfsva-0189, 7 pages.
  • N. K. Sudev and K. A. Germina, Weak Integer Additive Set- Indexers of Graph Operations, Global Journal of Mathematical Sciences: Theory and Practical, 6(1)(2014),25-36.
  • N. K. Sudev and K. A. Germina, Further Studies on the Sparing Number of Graphs, TechS Vidya e-Journal of Research, 2(2013-14), 28-38.
  • N. K. Sudev and K. A. Germina, A Note on Sparing Number of Graphs, Advances and Applications in Discrete Mathematics, 14(1)(2014), 51-65.
  • N. K. Sudev and K. A. Germina, On Weak Integer Additive Set-Indexers of Certain Graph Classes, Journal of Discrete Mathematical Sciences and Cryptography, to appear.
  • N. K. Sudev and K. A. Germina, Weak integer Additive Set- Indexers of Certain Graph Products, Journal of Informatics and Mathematical Sciences, 6(1)(2014), 35-43.
  • D BWest, (2001). Introduction to Graph Theory, Pearson Education Inc.