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Reseach Article

Weak Set-Labeling Number of Certain Integer Additive Set-Labeled Graphs

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

@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 },
issue_date = { March 2015 },
volume = { 114 },
number = { 2 },
month = { March },
year = { 2015 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume114/number2/19947-1772/ },
doi = { 10.5120/19947-1772 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:51:36.346320+05:30
%A N. K. Sudev
%A K. A. Germina
%A K. P. Chithra
%T Weak Set-Labeling Number of Certain Integer Additive Set-Labeled Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 114
%N 2
%P 1-6
%D 2015
%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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Index Terms

Computer Science
Information Sciences

Keywords

Integer additive set-labeled graphs weak integer additive setlabeled graphs weak set-labeling number of a graph.