Super edge-magic labeling of graphs: deficiency and maximality
| Main Authors: | Ngurah, Anak Agung Gede; Department of Civil Engineering University of Merdeka Malang Jalan Terusan Raya Dieng 62--64 Malang, Indonesia, Simanjuntak, Rinovia; Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesa 10 Bandung, Indonesia |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2017
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/367 http://www.ejgta.org/index.php/ejgta/article/view/367/pdf_50 |
Daftar Isi:
- A graph G of order p and size q is called super edge-magic if there exists a bijective function f from V(G) U E(G) to {1, 2, 3, ..., p+q} such that f(x) + f(xy) + f(y) is a constant for every edge $xy \in E(G)$ and f(V(G)) = {1, 2, 3, ..., p}. The super edge-magic deficiency of a graph G is either the smallest nonnegative integer n such that G U nK_1 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 graphs. We found a lower bound of the super edge-magic deficiency of join product of any connected graph with isolated vertices and a better upper bound of the super edge-magic deficiency of join product of super edge-magic graphs with isolated vertices. Also, we provide constructions of some maximal graphs, ie. super edge-magic graphs with maximal number of edges.