2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 219222
author:  Anna Lladó 

title:  Largest cliques in connected supermagic graphs 
keywords:  Labelings of graphs, magic graphs, Sidon sets. 
abstract: 
A graph
G=(V,E)
is said to be magic if there exists an
integer labeling
f: V∪E →[1, V∪E]
such that
f(x)+f(y)+f(xy)
is constant for all edges
xy∈E
. Enomoto, Masuda and Nakamigawa proved that there
are magic graphs of order at most
3n
which contain a complete graph of order
2
+o(n
2
)
n
. Bounds on Sidon sets show that the order of such a
graph is at least
n
. We close the gap between those two bounds by
showing that, for any given graph
2
+o(n
2
)
H
of order
n
, there are connected magic graphs of order
n
containing
2
+o(n
2
)
H
as an induced subgraph. Moreover it can be required
that the graph admits a supermagic labelling
f
, which satisfies the additional condition
f(V)=[1,V]
.

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reference:  Anna Lladó (2005), Largest cliques in connected supermagic graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 219222 
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