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Graphs isomorphic to subgraphs of their line-graphs

โœ Scribed by Douglas Bauer; Ralph Tindell

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
621 KB
Volume
41
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

An emhdding

of graph G into graph N is by definition an isomorphism OI G onto a subgraph of H. It is shown in this paper that every unicycle V embeds in its line-graph L(V), and that every other connected graph that embeds in its own line-graph may be constructed from such an embedded unicycle in a natural way. A complete, explicit classification is also given of the graphs G that admit a special kind of embedding into L(G), called an incidence embedding. Moreover, the question of which graphs G are isomorphic to induced subgraphs 6' of their line -graphs is shown to be formally equivalent to the original, more general question, where G' is not required to be induced.

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