2004/04/28 by Boris Hollas, Hollas, Boris
Mathematics · #05C80 #60C05 #92E10 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR #msc:05C80 #msc:60C05 #msc:92E10
paper · pdf · doi:10.48550/arxiv.math/0404512
arxiv created 2004/04/28 · arxiv updated 2009/12/01
We consider topological indices I that are sums of f(deg(u)) f(deg(v)), where u,v are adjacent vertices and f is a function. The Randić connectivity index or the Zagreb group index are examples for indices of this kind. In earlier work on topological indices that are sums of independent random variables, we identified the correlation between I and the edge set of the molecular graph as the main cause for correlated indices. We prove a necessary and sufficient condition for I having zero covariance with the edge set.