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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Pavel Tomasta, Eliška Tomová (1988)
Czechoslovak Mathematical Journal
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Faudree, Jill R., Faudree, Ralph J., Schmitt, John R. (2011)
The Electronic Journal of Combinatorics [electronic only]
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A. K. Dewdney, Frank Harary (1976)
Czechoslovak Mathematical Journal
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Vladislav Bína, Jiří Přibil (2015)
Commentationes Mathematicae Universitatis Carolinae
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The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split graphs.
Petrović, Miroslav (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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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...
Gliviak, Ferdinand, Kyš, P. (1997)
Acta Mathematica Universitatis Comenianae. New Series
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V. A., Ustimenko (2007)
Serdica Journal of Computing
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We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed...