Introduction to G-Graphs and their applications: a concise overview

Algebra has always played an important role in combinatorics, undoubtedly due to the power of the tools introduced by this theory. A significant portion of these developments concerns graphs and groups, and more specifically Cayley graphs, which are very useful in many scientific fields. This article presents a new type of graph associated with a group; more precisely, it is a survey that highlights the most important properties of this new type of graph. The relationships between G-graphs and Cayley graphs will be studied. Finally, some applications of these graphs will be examined.