In this thesis, we focused on the representation of graphs through the problem of universal graphs. A graph is an abstraction used to represent the interconnections between different objects; these objects are called vertices, and their connections are called edges. It is common to represent graphs as a matrix or as a list of vertex adjacencies. These traditional representations form the basis of graph algorithms, which are essential in many fields such as telecommunications, electronics, and computer science. However, in certain specific contexts—such as distributed computing—constraints on space and the number of communications necessitate the use of more compact, so-called implicit, representations. Labeling schemes address this challenge. An adjacency labeling scheme is, for a family of graphs, an assignment of labels to the vertices of the graphs in the family such that, given a pair of labels, and without any other information, it is possible to determine whether the corresponding vertices are adjacent or not. The goal, then, is to minimize the size of these labels. We have focused on this problem more specifically through a related problem: that of induced universal graphs and their minimum number of vertices. An induced universal graph for a family of graphs contains, as induced subgraphs—that is, by selecting only a subset of the graph’s vertices and all the edges connecting them—the set of all graphs in the family. The main results of this thesis concern the impossibility of constructing universal induced graphs for certain families of graphs using fewer than a certain number of vertices. These fairly general results allow us to provide lower bounds for families based on their characteristics, such as the number of graphs in the family or the presence of unions of complete graphs of a certain size within the family. We also studied the number of graphs needed to improve these lower bounds; this was achieved using a construction of universal induced graphs for small families of graphs, in particular subfamilies of minor-closed graphs such as planar graphs. We also present graph constructions induced universal graphs for various families, such as star forests and unions of complete graphs. For the latter, the construction we propose is optimal in terms of the number of vertices. Finally, we present complexity results for induced universal graphs of minimal size and generalize these results to other types of universal graphs.