A survey of minimum saturated graphs.
Faudree, Jill R., Faudree, Ralph J., Schmitt, John R. (2011)
The Electronic Journal of Combinatorics [electronic only]
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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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Brešar, Boštjan, Klavžar, Sandi, Škrekovski, Riste (2003)
The Electronic Journal of Combinatorics [electronic only]
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Josef Voldřich (1978)
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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.
Bagga, Jay (2004)
International Journal of Mathematics and Mathematical Sciences
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Stanislav Jendroľ, Vladimír Žoldák (1995)
Mathematica Slovaca
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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...
Liu, Guizhen, Qian, Jianbo, Sun, Jonathan Z., Xu, Rui (2008)
International Journal of Mathematics and Mathematical Sciences
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Ying Liu (2013)
Discussiones Mathematicae - General Algebra and Applications
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Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n₊,n₋,n₀) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n₀ denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n - 2ν(G). Guo et al. [Ji-Ming Guo, Weigen Yan and Yeong-Nan Yeh. On the nullity and the matching number...