Perkinson, David; Salter, Nick; Xu, Tianyuan A note on the critical group of a line graph. (English) Zbl 1218.05064 Electron. J. Comb. 18, No. 1, Research Paper P124, 6 p. (2011). Summary: This note answers a question posed by L. Levine in J. Comb. Theory, Ser. A 118, No. 2, 350–364 (2011; Zbl 1292.05135). The main result is Theorem 1 which shows that under certain circumstances a critical group of a directed graph is the quotient of a critical group of its directed line graph. Cited in 1 Document MSC: 05C20 Directed graphs (digraphs), tournaments 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C76 Graph operations (line graphs, products, etc.) Keywords:critical group; directed graph; directed line graph Citations:Zbl 1292.05135 PDFBibTeX XMLCite \textit{D. Perkinson} et al., Electron. J. Comb. 18, No. 1, Research Paper P124, 6 p. (2011; Zbl 1218.05064) Full Text: arXiv EuDML EMIS