Old and new generalizations of line graphs
Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge-isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations. In its long history, the concept has...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204310094 |
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| author | Jay Bagga |
| author_facet | Jay Bagga |
| author_sort | Jay Bagga |
| collection | DOAJ |
| description | Line graphs have been studied for over seventy years. In 1932, H.
Whitney showed that for connected graphs, edge-isomorphism
implies isomorphism except for K3 and K1,3. The line
graph transformation is one of the most widely studied of all
graph transformations. In its long history, the concept has been
rediscovered several times, with different names such as derived
graph, interchange graph, and edge-to-vertex dual. Line graphs
can also be considered as intersection graphs. Several variations
and generalizations of line graphs have been proposed and
studied. These include the concepts of total graphs, path graphs,
and others. In this brief survey we describe these and some more
recent generalizations and extensions including super line graphs
and triangle graphs. |
| format | Article |
| id | doaj-art-28a88134226e4586b9bb5f8372018dae |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-28a88134226e4586b9bb5f8372018dae2025-02-03T01:20:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004291509152110.1155/S0161171204310094Old and new generalizations of line graphsJay Bagga0Department of Computer Science, Ball State University, Muncie 47306, IN, USALine graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge-isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations. In its long history, the concept has been rediscovered several times, with different names such as derived graph, interchange graph, and edge-to-vertex dual. Line graphs can also be considered as intersection graphs. Several variations and generalizations of line graphs have been proposed and studied. These include the concepts of total graphs, path graphs, and others. In this brief survey we describe these and some more recent generalizations and extensions including super line graphs and triangle graphs.http://dx.doi.org/10.1155/S0161171204310094 |
| spellingShingle | Jay Bagga Old and new generalizations of line graphs International Journal of Mathematics and Mathematical Sciences |
| title | Old and new generalizations of line graphs |
| title_full | Old and new generalizations of line graphs |
| title_fullStr | Old and new generalizations of line graphs |
| title_full_unstemmed | Old and new generalizations of line graphs |
| title_short | Old and new generalizations of line graphs |
| title_sort | old and new generalizations of line graphs |
| url | http://dx.doi.org/10.1155/S0161171204310094 |
| work_keys_str_mv | AT jaybagga oldandnewgeneralizationsoflinegraphs |