Research Article
Weak Set-Labeling Number of Certain Integer Additive Set-Labeled Graphs
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 114 - Issue 2 |
| Published: March 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
@article{ 10.5120/19947-1772,
author = { N. K. Sudev,K. A. Germina,K. P. Chithra },
title = { Weak Set-Labeling Number of Certain Integer Additive Set-Labeled Graphs },
journal = { International Journal of Computer Applications },
year = { 2015 },
volume = { 114 },
number = { 2 },
pages = { 1-6 },
doi = { 10.5120/19947-1772 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2015
%A N. K. Sudev
%A K. A. Germina
%A K. P. Chithra
%T Weak Set-Labeling Number of Certain Integer Additive Set-Labeled Graphs%T
%J International Journal of Computer Applications
%V 114
%N 2
%P 1-6
%R 10.5120/19947-1772
%I Foundation of Computer Science (FCS), NY, USA
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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