A graph made by substituting a module into a word-representable graph is word-representable if and only if the module is a comparability graph, yielding a characterization of lexicographic products.
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Characterization of Word-Representable Graphs using Modular Decomposition
A graph made by substituting a module into a word-representable graph is word-representable if and only if the module is a comparability graph, yielding a characterization of lexicographic products.