Abstract
An Eulerian circuit in a connected graph G is a circuit that contains every edge of G exactly once while an Eulerian walk in G is a closed walk that contains every edge of G at least once. While only Eulerian graphs contain an Eulerian circuit, every nontrivial connected graph contains an Eulerian walk. The irregularity concept here is an irregular Eulerian walk in G, which is an Eulerian walk where no two edges of G are encountered the same number of times. The irregularity counterpart for vertices is a Hamiltonian walk. These are the primary topics for this chapter.
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Ali, A., Chartrand, G., Zhang, P. (2021). Traversable Irregularity. In: Irregularity in Graphs. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-67993-4_7
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DOI: https://doi.org/10.1007/978-3-030-67993-4_7
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