Old and new generalizations of line graphs.
Bagga, Jay (2004)
International Journal of Mathematics and Mathematical Sciences
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Bagga, Jay (2004)
International Journal of Mathematics and Mathematical Sciences
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Simic, Slobodan K. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Juraj Bosák (1984)
Mathematica Slovaca
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Vladimír Baláž, Vladimír Kvasnička, Jiří Pospíchal (1989)
Časopis pro pěstování matematiky
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Abdollah Khodkar, Rui Xu (2007)
Discussiones Mathematicae Graph Theory
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In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max{a+1,an/(a+b) + a - 2} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction...
Gutman, I. (1996)
Publications de l'Institut Mathématique. Nouvelle Série
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A. K. Dewdney, Frank Harary (1976)
Czechoslovak Mathematical Journal
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Carmi, Paz, Dujmovic, Vida, Morin, Pat, Wood, David R. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Jaroslav Ivanco (2007)
Discussiones Mathematicae Graph Theory
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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.