strongly regular graphs
A strongly regular graph is a type of graph characterized by specific parameters that define its structure. It is defined by three parameters: n (the number of vertices), k (the number of edges connected to each vertex), and \lambda and \mu (which describe the number of common neighbors between pairs of adjacent and non-adjacent vertices, respectively). This means that every vertex has the same number of connections, and the relationships between vertices are uniform.
These graphs are important in various fields, including combinatorics and network theory, because they exhibit regularity and symmetry. Strongly regular graphs can be used to model situations where uniform connectivity is essential, such as in error-correcting codes and design theory. Their structured nature allows for easier analysis and understanding of complex networks.