On (super) edge-magic deficiency of some classes of graphs

Ngurah, Anak Agung Gede (Universitas Merdeka Malang)
Simanjuntak, Rinovia (Institut Teknologi Bandung)
Baskoro, Edy Tri (Institut Teknologi Bandung)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications

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.