On the super edge-magic deficiency of join product and chain graphs

Anak Agung Gede Ngurah, Rinovia Simanjuntak

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(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.


Keywords


super edge-magic graph, super edge magic deficiency, join product graph, chain graph

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DOI: http://dx.doi.org/10.5614/ejgta.2019.7.1.12

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