Abstract
An edgee of a graphG is called a fixed edge if G −e +e′ ≅ G impliese′ = e, and an isomorphic fixed edge if G −e + e′ ≅ G implies that there exists an automorphism of G −e, which maps the ends ofe to the ends ofe′. It is proved that almost every graph is with all its edges as fixed edges and isomorphic fixed edges, and it is conjectured that all graphs contain isomorphic fixed edges.
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Fan, H. Almost every graph has a fixed edge. Chin. Sci. Bull. 43, 99–101 (1998). https://doi.org/10.1007/BF02883915
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DOI: https://doi.org/10.1007/BF02883915