Structures How Many Isomers Has Decane

In this subsection, we briefly summarize results relevant to labeled graphs. We then survey the work on counting series by Cayley, Polya, Ffarary, 

We first note that 2 = ( —l)/2 possible distinct edges exist 

As the objects we are interested in this chapter are connected, let Ck be the number of connected labeled graphs of k vertices. kC rooted connected labeled graphs exist because k ways exist of choosing a root. The number of rooted, labeled graphs of n vertices in which the root is in a connected component containing k vertices is feQ ( This expression, summed from 

Interestingly enough, investigations related to counting unlabeled graphs started with the pragmatic problem of calculating the number of paraffin 

Theorem (Polya). The configuration generating function, or counting series, C(x), is obtained by substituting the figure generating function, c(x), in the cycle index, by replacing every occurrence of Sk in the cycle index by c x ). Thus, 

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