Covering and Euler cycles on non-oriented graphs

A covering cycle is a closed path that traverses each edge of a graph at least once. Two cycles are equivalent if one is a cyclic permutation of the other. We compute the number of equivalence classes of non-periodic covering cycles of given length in a non-oriented connected graph. A special case i...

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Bibliographic Details
Published in:Periodica mathematica Hungarica 2018-12, Vol.77 (2), p.201-208
Main Authors: da Costa, G. A. T. F., Policarpo, M.
Format: Article
Language:English
Subjects:
Equivalence
Mathematics
Mathematics and Statistics
Permutations
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Summary:A covering cycle is a closed path that traverses each edge of a graph at least once. Two cycles are equivalent if one is a cyclic permutation of the other. We compute the number of equivalence classes of non-periodic covering cycles of given length in a non-oriented connected graph. A special case is the number of Euler cycles (covering cycles that cover each edge of the graph exactly once) in the non-oriented graph. We obtain an identity relating the numbers of covering cycles of any length in a graph to a product of determinants.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-018-0235-2