On (super) edge-magic deficiency of some classes of graphs - Ngurah, Anak Agung Gede; Simanjuntak, Rinovia; Baskoro, Edy Tri (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
A graph G of order p and size q is called edge-magic total if there exists a bijection ϕ from V(G)∪E(G) to the set 1, 2, …, p + q such that ϕ(s)+ϕ(st)+ϕ(t) is a constant for every edge st in E(G). An edge-magic total graph with ϕ(V(G)) = 1, 2, …, p is called super edge-magic total. Furthermore, the edge-magic deficiency of a graph G is the smallest integer n ≥ 0 such that G ∪ nK1 is edge-magic total. The super edge-magic deficiency of a graph G is either the smallest integer n ≥ 0 such that G ∪ nK1 is super edge-magic total or +∞ if there exists no such integer n. In this paper, we study the (super) edge-magic deficiency of join product graphs and 2-regular graphs.