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Weak Set-Labeling Number of Certain Integer Additive Set-Labeled Graphs
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 114 - Number 2 |
| Year of Publication: 2015 |
| Authors: N. K. Sudev, K. A. Germina, K. P. Chithra |
10.5120/19947-1772
|
N. K. Sudev, K. A. Germina, K. P. Chithra . Weak Set-Labeling Number of Certain Integer Additive Set-Labeled Graphs. International Journal of Computer Applications. 114, 2 ( March 2015), 1-6. DOI=10.5120/19947-1772
Abstract
Let N0 be the set of all non-negative integers, let X N0 and P(X) be the the power set of X. An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) ! P(N0) such that the induced function f+ : E(G) ! P(N0) is defined by f+(uv) = f(u) + f(v), where f(u) + f(v) is the sum set of f(u) and f(v). An IASL f is said to be an integer additive set-indexer (IASI) of a graph G if the induced edge function f+ is also injective. An integer additive set-labeling f is said to be a weak integer additive set-labeling (WIASL) if jf+(uv)j = max(jf(u)j; jf(v)j) 8 uv 2 E(G). The minimum cardinality of the ground setX required for a given graph G to admit an IASL is called the set-labeling number of the graph. In this paper, the notion of the weak set-labeling number of a graph G is introduced as the minimum cardinality of X so that G admits a WIASL with respect to the ground set X and the weak set-labeling numbers of certain graphs are discussed.
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