Correlation of graph-theoretical indices

The correlation of graph characteristics, such as the number of independent vertex or edge subsets, the number of connected subsets, or the sum of distances, which also play a role in combinatorial chemistry, is studied by a generating function approach and asymptotic analysis. It is shown how an asymptotic formula for the correlation coefficient can be obtained when simply generated families of trees are investigated. For rooted ordered trees, the calculations are done explicitly. Further feasible correlation measures are discussed.