https://hal.inria.fr/hal-01184371Lladó, AnnaAnnaLladóUPC - Universitat Politècnica de Catalunya [Barcelona]Largest cliques in connected supermagic graphsHAL CCSD2005Labelings of graphsmagic graphsSidon sets[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]Episciences Iam, CoordinationStefan Felsner2015-08-14 11:38:012020-11-16 15:56:032015-08-14 16:38:21enConference papershttps://hal.inria.fr/hal-01184371/document10.46298/dmtcs.3414application/pdf1A 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 $f(V)=[1,|V|]$.