A word-representable graph is a graph for which there is a word on its vertex set such
that two distinct letters alternate in the word
precisely when the corresponding vertices are adjacent.
A representing word is 
-uniform if every graph vertex
occurs exactly 
times. The least such 
is the representation
number 
.
Akgün et al. (2019) enumerated the connected graphs that are not word-representable. For 
, 2, ..., their numbers begin 0, 0, 0, 0, 0, 1, 25, 929,
54957, 4880093, 650856040, ... (OEIS A290814).
A non-word-representable graph is minimal when every proper induced
subgraph is word-representable. For 
, 6, ..., the numbers of minimal examples begin 0, 1, 10,
47, 179, ... (OEIS A319491).
