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Strong Integer Additive Set-Valued Graphs: A Creative Review

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International Journal of Computer Applications
© 2015 by IJCA Journal
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 and K P Chithra. Article: Strong Integer Additive Set-Valued Graphs: A Creative Review. International Journal of Computer Applications 115(4):1-7, April 2015. Full text available. BibTeX

@article{key:article,
	author = {N. K. Sudev and K. A. Germina and K. P. Chithra},
	title = {Article: Strong Integer Additive Set-Valued Graphs: A Creative Review},
	journal = {International Journal of Computer Applications},
	year = {2015},
	volume = {115},
	number = {4},
	pages = {1-7},
	month = {April},
	note = {Full text available}
}

Abstract

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.

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