Superstable graphs
Heinrich Herre, Allan Mekler, Kenneth Smith (1983)
Fundamenta Mathematicae
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Heinrich Herre, Allan Mekler, Kenneth Smith (1983)
Fundamenta Mathematicae
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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.
Lawrence Moss (1989)
Fundamenta Mathematicae
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I.B. Lackovic, D.M. Cvetkovic (1976)
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Jerzy Topp (1990)
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Izak Broere, Johannes Heidema (2013)
Discussiones Mathematicae Graph Theory
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The well-known Rado graph R is universal in the set of all countable graphs I, since every countable graph is an induced subgraph of R. We study universality in I and, using R, show the existence of 2 א0 pairwise non-isomorphic graphs which are universal in I and denumerably many other universal graphs in I with prescribed attributes. Then we contrast universality for and universality in induced-hereditary properties of graphs and show that the overwhelming majority of induced-hereditary...