Abstract: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.
Keywords: graph enumeration; labeled graph; split graph
DOI: DOI 10.14712/1213-7243.2015.112
AMS Subject Classification: 05C30 05A15