Anna Lladó

Largest cliques in connected supermagic graphs
dmtcs:3414 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

https://doi.org/10.46298/dmtcs.3414
Largest cliques in connected supermagic graphs
Authors: Anna Lladó ^{1}
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Anna Lladó
1 Universitat Politècnica de Catalunya [Barcelona]
A graph $G=(V,E)$ is said to be $\textit{magic}$ if there exists an integer labeling $f: V \cup E \to [1, V \cup E]$ such that $f(x)+f(y)+f(xy)$ is constant for all edges $xy \in E$. Enomoto, Masuda and Nakamigawa proved that there are magic graphs of order at most $3n^2+o(n^2)$ which contain a complete graph of order $n$. Bounds on Sidon sets show that the order of such a graph is at least $n^2+o(n^2)$. We close the gap between those two bounds by showing that, for any given graph $H$ of order $n$, there are connected magic graphs of order $n^2+o(n^2)$ containing $H$ as an induced subgraph. Moreover it can be required that the graph admits a supermagic labelling $f$, which satisfies the additional condition $f(V)=[1,V]$.