Shift graphs and generalized shift graphs are word-representable, yielding families of graphs whose line graphs are not word-representable (for >=5 vertices) while their line digraphs are.
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Word-Representability of Shift Graphs
Shift graphs and generalized shift graphs are word-representable, yielding families of graphs whose line graphs are not word-representable (for >=5 vertices) while their line digraphs are.