A combinatorial trace method: Counting closed walks to assay graph eigenvalues

D’Souza, Keith; Krebs, Mike

doi:10.1216/rmj-2013-43-2-469

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Counting Covering and Euler Cycles1

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“…Some years back I asked Prof. Michael Krebs (State University of California) [6] if he knew how, along the lines of the combinatorial trace method [5], to compute the number of covering cycles of a given length in a graph. Few days later he replied and his ideas are encapsulated in Theorem 2.1.…”

Section: Counting Covering and Euler Cyclesmentioning

confidence: 99%

Counting covering cycles

da Costa,

Policarpo

2015

Preprint

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We compute the number of equivalence classes of nonperiodic covering cycles of given length in a non oriented connected graph. A covering cycle is a closed path that traverses each edge of the graph at least once. A special case is the number of Euler cycles in the non oriented graph. An identity relating the numbers of covering cycles of any length in a graph to a product of determinants is obtained.

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Section: Counting Covering and Euler Cyclesmentioning

confidence: 99%