Do you have all $k^n$ strings of length $n$ using your $k$ symbol alphabet or a selection such as all consecutive 30 letter strings found in the DNA of some individual. The former is a Hamming graph but the latter is "subgraph of a Hamming graph" and I'm not sure how easy it is to say if a given graph can be realized in this way. Although there are restrictions.

Define a "line" to be any maximal clque (set of adjacent points) then 2 points are on at most one line. Then lines have size $k$ or less. Planes are less clear to me.

Do you have all $k^n$ strings of length $n$ using your $k$ symbol alphabet or a selection such as all consecutive 30 letter strings found in the DNA of some individual. The former is a Hamming graph but the latter is "subgraph of a Hamming graph" and I'm not sure how easy it is to say if a given graph can be realized in this way. Although there are restrictions.

Define a "line" to be any maximal clque (set of adjacent points) then 2 points are on at most one line. Then lines have size $k$ or less. Planes are less clear to me.

As commented elsewhere, quasi-Hamming is defined to have the additional condition that distances are the same as in a full Hamming graph so if you have AAAAA and AAABC then you must have one or both of AAABA and AAAAC. There can be triangles and (AAA,BAA,BAX,BCX,BCY,ACY,ACA) would make a cord free $7$-gon. However there can not be a cord free $5$-gon.

Do you have all $k^n$ strings of length $n$ using your $k$ symbol alphabet or a selection such as all consecutive 30 letter strings found in the DNA of some individual. The former is a Hamming graph but the latter is "subgraph of a Hamming graph" and I'm not sure how easy it is to say if a given graph can be realized in this way. Certainly given an edge the vertices adjacent to both ends are all adjacent to each other. So one could call any maximal clique a "line" and two points determine at most one line. One can see how to define "planes" etc.

Do you have all $k^n$ strings of length $n$ using your $k$ symbol alphabet or a selection such as all consecutive 30 letter strings found in the DNA of some individual. The former is a Hamming graph but the latter is "subgraph of a Hamming graph" and I'm not sure how easy it is to say if a given graph can be realized in this way. Although there are restrictions.

Define a "line" to be any maximal clque (set of adjacent points) then 2 points are on at most one line. Then lines have size $k$ or less. Planes are less clear to me.