On the super edge-magic deficiency of join product and chain graphs - Anak Agung Gede Ngurah; Rinovia Simanjuntak (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2019)
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(xy) + f(y) is a constant for every edge xy ∈ E(G) and f(V(G)) = 1, 2, 3, ⋯, p. Furthermore, the super edge-magic deficiency of a graph G, μs(G), is either the minimum nonnegative integer n such that G ∪ nK1 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.