A study on topogenic integer additive set-labeled graphs
Résumé
Let N 0 denote the set of all non-negative integers and P(N 0) be its power set. 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 sumset of f (u) and f (v). The IASL f is said to be an integer additive set-indexer (IASI) if the associated function f + is also injective. If f + (uv) = k ∀ uv ∈ E(G), then f is said to be a k-uniform integer additive set-indexer. In this paper, we study the admissibility of a particular type of integer additive set-labeling, called topogenic IASL, by certain graphs.
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