On the number of Euler trails in directed graphs

Authors

  • Jakob Jonsson

DOI:

https://doi.org/10.7146/math.scand.a-14370

Abstract

Let G be an Eulerian digraph with all in- and out-degrees equal to 2, and let π be an Euler trail in G. We consider an intersection matrix L(π) with the property that the determinant of L(π)+I is equal to the number of Euler trails in G; I denotes the identity matrix. We show that if the inverse of L(π) exists, then L1(π)=L(σ) for a certain Euler trail σ 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.

Downloads

Published

2002-06-01

How to Cite

Jonsson, J. (2002). On the number of Euler trails in directed graphs. MATHEMATICA SCANDINAVICA, 90(2), 191–214. https://doi.org/10.7146/math.scand.a-14370

Issue

Section

Articles