Counting covering cycles
G.A.T.F da Costa, M. Policarpo

TL;DR
This paper develops a method to count equivalence classes of nonperiodic covering cycles in graphs, relating these counts to determinants, and includes special cases like Euler cycles.
Contribution
It introduces a novel identity linking covering cycle counts to determinants, expanding understanding of cycle enumeration in graphs.
Findings
Derived an explicit formula for counting covering cycles.
Established a determinant-based identity for cycle enumeration.
Connected covering cycle counts to Euler cycles in graphs.
Abstract
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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Taxonomy
TopicsLimits and Structures in Graph Theory · semigroups and automata theory · Cellular Automata and Applications
