Year: 2025
Type: article
Abstract: Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. Dénes proved that the permutation is a full cyclic permutation for any linear order if and only if the graph is a tree. In this article, we characterize graphs having a linear order such that the associated permutation is a full cyclic permutation in terms of graph embeddings. Moreover, we give a counter example for Eden's question about an edge ordering whose associated permutation is the identity.
Authors: Tsujie, Shuhei, Uchiumi, Ryo
Institutions: Hokkaido University of Education, The University of Osaka
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7115341051
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