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A note on the critical group of a line graph. (English) Zbl 1218.05064

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.

MSC:

05C20 Directed graphs (digraphs), tournaments
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C76 Graph operations (line graphs, products, etc.)

Citations:

Zbl 1292.05135
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