Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications

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

Anak Agung Gede Ngurah (Department of Civil Engineering, Universitas Merdeka Malang, Jalan Terusan Raya Dieng 62-64 Malang, Indonesia)
Rinovia Simanjuntak (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia)

Article Info

Publish Date
05 Apr 2019

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.

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Journal Info
Electronic Journal of Graph Theory and Applications (EJGTA)
Website

Abbrev

ejgta

Publisher

Indonesian Combinatorial Society

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...