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On the number of Euler trails in directed graphs
2002 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 90, no 2, 191-214 p.Article in journal (Refereed) Published
Abstract [en]

Let G be an Eulerian digraph with all in- and out-degrees equal to 2, and let pi be an Euler trail in G. We consider an intersection matrix L(pi) with the property that the determinant of L(pi) + I is equal to the number of Euler trails in G; I denotes the identity matrix. We show that if the inverse of L(pi) exists, then L-1 (pi) = L(sigma) for a certain Euler trail sigma in G. Furthermore, we use properties of the intersection matrix to prove some results about how to divide the set of Euler trails in a digraph into smaller sets of the same size.

Place, publisher, year, edition, pages
2002. Vol. 90, no 2, 191-214 p.
Keyword [en]
digraphs, formula
Identifiers
URN: urn:nbn:se:kth:diva-21736ISI: 000176987500003OAI: oai:DiVA.org:kth-21736DiVA: diva2:340434
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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