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

Anak Agung Gede Ngurah, Rinovia Simanjuntak, Edy Tri Baskoro

Abstract


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.

Keywords


(super) edge-magic graph; (super) edge-magic deficiency; join product; 2-regular graph

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DOI: http://dx.doi.org/10.5614/ejgta.2025.13.1.4

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