CFP last date

by
N. K. Sudev,
K. A. Germina,
K. P. Chithra

International Journal of Computer Applications |

Foundation of Computer Science (FCS), NY, USA |

Volume 115 - Number 4 |

Year of Publication: 2015 |

Authors: N. K. Sudev, K. A. Germina, K. P. Chithra |

10.5120/20136-2254 |

N. K. Sudev, K. A. Germina, K. P. Chithra . Strong Integer Additive Set-Valued Graphs: A Creative Review. International Journal of Computer Applications. 115, 4 ( April 2015), 1-7. DOI=10.5120/20136-2254

@article{
10.5120/20136-2254,

author = {
N. K. Sudev,
K. A. Germina,
K. P. Chithra
},

title = { Strong Integer Additive Set-Valued Graphs: A Creative Review },

journal = {
International Journal of Computer Applications
},

issue_date = { April 2015 },

volume = { 115 },

number = { 4 },

month = { April },

year = { 2015 },

issn = { 0975-8887 },

pages = {
1-7
},

numpages = {9},

url = {
https://ijcaonline.org/archives/volume115/number4/20136-2254/
},

doi = { 10.5120/20136-2254 },

publisher = {Foundation of Computer Science (FCS), NY, USA},

address = {New York, USA}

}

%0 Journal Article

%1 2024-02-06T22:53:48.656740+05:30

%A N. K. Sudev

%A K. A. Germina

%A K. P. Chithra

%T Strong Integer Additive Set-Valued Graphs: A Creative Review

%J International Journal of Computer Applications

%@ 0975-8887

%V 115

%N 4

%P 1-7

%D 2015

%I Foundation of Computer Science (FCS), NY, USA

For a non-empty ground set X, finite or infinite, the set-valuation or set-labeling of a given graph G is an injective function f : V (G) ! P(X) such that the induced edge-function f : E(G) ! P(X) ?? f;g is defined by f (uv) = f(u) f(v) for every uv2E(G), where P(X) is the power set of the set X and is a binary operation on sets. A set-indexer of a graph G is an set-labeling f : V (G) such that the edge-function f is also injective. An integer additive set-labeling (IASL) of a graph G is defined as an injective function f : V (G) ! P(N0) such that the induced edge-function gf : E(G) ! P(N0) is defined by gf (uv) = f(u) + f(v), where N0 is the set of all non-negative integers, P(N0) is its power set and f(u)+f(v) is the sumset of the set-labels of two adjacent vertices u and v in G. An IASL f is said to be a strong IASL if jf+(uv)j = jf(u)j jf(v)j for every pair of adjacent vertices u; v in G. In this paper, the characteristics and properties of strong integer additive set-labeled graphs are critically and creatively reviewed.

- 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.
- B. D. Acharya, Set-Indexers of a Graph and Set-Graceful Graphs, Bull. Allahabad Mathematical Society, 16(2001), 1- 23.
- B. D. Acharya and K. A. Germina, Strongly Indexable Graphs: Some New Perspectives, Advanced Modelling and Optimisation, 15(1)(2013), 3-22.
- T. M. K. Anandavally, A Characterisation of 2-Uniform IASI Graphs, International Journal of Contemporary Mathematical Sciences, 8(10)(2013), 459-462.
- T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1989.
- M. Behzad, The connectivity of Total Graphs, Bulletin of Australian Mathematical Society, 1(1969), 175-181.
- J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Macmillan Press, London, 1976.
- J. A. Bondy and U. S. R. Murty, Graph Theory, Springer, 2008.
- A. Brandst¨adt, V. B. Le and J. P. Spinrad, Graph Classes:A Survey, SIAM, Philadelphia, 1999.
- A. Brand¨adt, P. L. Hammer, V. B. Le and V. L. Lozin, Bisplit graphs, Discrete Mathematics, 299(1-3)(2005), 11-32.
- D. M. Burton, Elementary Number Theory, Tata McGraw- Hill Inc. , New Delhi, 2007.
- M. Capobianco and J. Molluzzo, Examples and Counterexamples in Graph Theory, North-Holland, New York, 1978.
- N. Deo, Graph theory With Application to Engineering and Computer Science, Prentice Hall, India, 1974.
- R. Frucht and F. Harary, On the Corona of Two Graphs, Aequationes Mathemaematica, 4(3)(1970), 322-325.
- J. A. Gallian, A Dynamic Survey of Graph Labelling, The Electronic Journal of Combinatorics (DS #6), 2011.
- 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, N. K. Sudev, On Weakly Uniform Integer Additive Set-Indexers of Graphs, International Mathematical Forum, 8(37-40)(2013), 1827-1834.
- J. T. Gross and J. Yellen, Graph Theory and its Applications, CRC Press, 2006.
- G Hahn and G Sabidussi, Graph Symmetry: Algebraic Methods and Applications, NATO Advanced Science Institute Series-C 497, Springer, 1997.
- R. Hammack,W. Imrich and S. Klavzar, Handbook of Product graphs, CRC Press, 2011.
- F. Harary, Graph Theory, Addison-Wesley, 1969.
- K. D. Joshi, Applied Discrete Structures, New Age International, New Delhi, 2003.
- M B Nathanson, Additive Number Theory, Inverse Problems and Geometry of Sumsets, Springer, New York, 1996.
- M B Nathanson, Elementary Methods in Number Theory, Springer-Verlag, New York, 2000.
- M B Nathanson, Additive Number Theory: The Classical Bases, Springer-Verlag, New York, 1996.
- A. Rosa, On certain valuation of the vertices of a graph, in Theory of Graphs, Gordon and Breach, 1967.
- N. K. Sudev and K. A. Germina, On Integer Additie Set- Indexers of Graphs, International Journal Mathematical Sciences and Engineering Applications, 8(2)(2014), 11-22.
- N. K. Sudev and K. A. Germina, Some New Results on Strong Integer Additive Set-Indexers of Graphs, Discrete Mathematics Algorithms and Applications, 7(1)(2015), 11 pages.
- N. K. Sudev and K. A. Germina, (2014). A Characterisation of Strong Integer Additive Set-Indexers of Graphs, Communications in Mathematics and Applications, 5(3), 101-110.
- N. K. Sudev and K. A. Germina, A Study on the Nourishing Number of Graphs and Graph Powers, Mathematics, 3(1)(2015), 29-40 .
- E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC press, 2011.
- D B West, Introduction to Graph Theory, Pearson Education Inc. , 2001.
- Information System on Graph Classes and their Inclusions, http://www. graphclasses. org/smallgraphs.

Computer Science

Information Sciences