Suppose that a graph G has vertices A, B, C, and D such that A is adjacent to each of B, C, and D, but {B, C, D} is an independent set. Then G cannot be a line graph.
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Suppose that a graph G has vertices A, B, C, and D such that A is adjacent to each of B, C, and D, but {B, C, D} is an independent set. Then G cannot be a line graph.
Source: wiktionary