Hamming graphs are a type of graph used in combinatorial mathematics and coding theory. They are constructed based on the concept of Hamming distance, which measures how different two strings of equal length are. In a Hamming graph, vertices represent strings of a fixed length over a given alphabet, and edges connect vertices that differ by a specific number of bits. These graphs are useful for studying error-correcting codes and network design. The structure of Hamming graphs allows researchers to analyze properties like connectivity and diameter, which are important for understanding how information can be transmitted reliably in communication systems.