Year: 2015
Type: article
Abstract: Let N 0 be the set of all non-negative integers, let X ⊂ N 0 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(N 0 ) such that the induced function f + : E(G) → P(N 0 ) 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 |f + (uv)| = max(|f (u)|, |f (v)|) ∀ uv ∈ E(G).The minimum cardinality of the ground set X 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.
DOI: 10.5120/19947-1772
Authors: N. K.Sudev, K. A. Germina, K. P. Chithra
Institution: Mary Matha Arts and Science College
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2417426730