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Strong Integer Additive Set-Valued Graphs: A Creative Review
| 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
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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