Line graph: Difference between revisions

Revision as of 08:41, 27 September 2023

Revision as of 20:57, 6 November 2023

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| jstor = 2039666

}}. {{Citation

| last = Las Vergnas | first = M. | authorlinkauthor-link = Michel Las Vergnas

| mr = 0412042

| issue = 2–3–4

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An alternative construction, the [[medial graph]], coincides with the line graph for planar graphs with maximum degree three, but is always planar. It has the same vertices as the line graph, but potentially fewer edges: two vertices of the medial graph are adjacent if and only if the corresponding two edges are consecutive on some face of the planar embedding. The medial graph of the [[dual graph]] of a plane graph is the same as the medial graph of the original plane graph.<ref>{{citation

| last = Archdeacon | first = Dan | authorlinkauthor-link = Dan Archdeacon

| doi = 10.1016/0012-365X(92)90328-D

| issue = 2

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| volume = 80

| issue = 1

| pagespage = 016105

| doi = 10.1103/PhysRevE.80.016105| pmid = 19658772

| bibcode = 2009PhRvE..80a6105E}}.

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| s2cid = 122473974 | hdl-access = free

}}.

*{{citation|first=F.|last=Harary|authorlinkauthor-link=Frank Harary|title=Graph Theory|publisher=Addison-Wesley|___location=Massachusetts|year=1972|url=http://www.dtic.mil/dtic/tr/fulltext/u2/705364.pdf|contribution=8. Line Graphs|pages=71–83|access-date=2013-11-08|archive-date=2017-02-07|archive-url=https://web.archive.org/web/20170207091815/http://www.dtic.mil/dtic/tr/fulltext/u2/705364.pdf|url-status=dead}}.

*{{citation

| last1 = Hemminger | first1 = R. L.

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| year = 1982}}.

*{{citation

| last = Trotter | first = L. E., Jr.

| doi = 10.1007/BF01593791

| issue = 2