On the super edge-magic deficiency of forests (original) (raw)

PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations

Let G = (V, E) be a finite and simple graph with vertex set V (G) and edge set E(G), having o rder p and size q. A graph G is called super edge-magic if there exists a bijection f : V(G) ∪ E(G) −→ {1, 2, • • • , p + q} such that f (V(G)) = {1, 2, • • • , p} and f (u) + f (uv) + f (v) = k, for every edge uv ∈ E(G). The super edge-magic deficiency of a graph G, denoted by μ s (G), is either the minimum nonnegative integer n such that G ∪ nK 1 is super edge-magic or +∞ if there exists no such n. In this paper, we study the super edge-magic deficiency of forests where its components are subdivided stars or paths.

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