Abstract
A graph G of order ∣ V ( G )∣ = p and size ∣ E ( G )∣ = q is called super edge-magic if there exists a bijection f : V ( G ) ∪ E ( G ) → {1, 2, 3, ⋯, p + q } such that f ( x ) + f ( x y ) + f ( y ) is a constant for every edge x y ∈ E ( G ) and f ( V ( G )) = {1, 2, 3, ⋯, p } . Furthermore, the super edge-magic deficiency of a graph G , μ s ( G ) , is either the minimum nonnegative integer n such that G ∪ n K 1 is super edge-magic or + ∞ if there exists no such integer n . In this paper, we study the super edge-magic deficiency of join product of a graph which has certain properties with an isolated vertex and the super edge-magic deficiency of chain graphs.
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