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New proofs for Levine’s theorems

✍ Scribed by Iwao Sato

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
215 KB
Volume
435
Category
Article
ISSN
0024-3795

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✦ Synopsis

Recently, Levine [9] expressed the vertex weighted complexity on spanning trees (with a fixed root) of the directed line graph of a digraph D in terms of the edge weighted complexity on spanning trees (with a fixed root) of D. We present new proofs for two Levine's Theorems. Furthermore, we express the number of unicycles of the directed line graph of a digraph D in terms of the number of unicycles of D.

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