Eulerian path

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Eulerian path

[ȯi′ler·ē·ən ′path]
(mathematics)
A path that traverses each of the lines in a graph exactly once.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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An Eulerian cycle in the graph of a pattern cyclic class can be realized by a sequence of values if and only if the order relations implied by the individual edges form a directed acyclic graph, and thus can be extended to a partial order, as then any extension to a total order will provide a realisation of a universal cycle.
We will show how to select an Eulerian cycle in G([Av.sub.n](123, 3142, 3412)) in a careful way which allows the construction of a universal cycle.
Because of the trace, one has to draw Eulerian cycles on the graphs after some vertex identifications.
Graph theory including directed graphs, Eulerian cycles, and Hamiltonian paths are typical content in upper secondary general or further mathematics subjects.