Abstract
Line graphs of simple graphs have been widely studied in the past 30 years. This paper discusses the line graphs with parallel edges or (and) loops. The conditions of a graph to be a line graph are given, and the formulas for determining the number of edges of a line graph in each case are derived. The public recognized forbidden subgraphs of line graphs are reduced from 9 to 3. The forbidden sub-digraphs are also found. >
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