I have a set of unique strings (with an alphabet size of >=4) of equal length to represent the vertices (not all possible strings are represented in the graph). I have an edge between a pair of vertices if the Hamming distance between the two strings is 1.

I have an interest in graphs and how they can be use in my biological research. So I've been trying to find out the name of this type of graph so I can try to understand more about it and how such graphs can be constructed and analysed efficiently for graphs with a large number of vertices (in the order of 100's of thousands to millions). However, I have no formal training in Maths so I'm finding it difficult to understand the formal language often used to describe graphs.

So far I've seen mention of Hamming Graph, Complete Hamming Graph, Partial Hamming Graphs and others. Your guidance would be most invaluable!