Abstract
In this paper, we first establish a version of the central limit theorem for a double sequence {pi(n)} that satisfies a linear recurrence relation. Then we find and prove that under some commonly observed conditions, the sequence of embedding distributions of an H-linear family of graphs with spiders is asymptotic to a normal distribution. Applications are given to some well-known path-like and ring-like sequences of graphs. We also prove that the limit for the Euler-genus distributions of a sequence of graphs is the same as the limit for the crosscap-number distributions of that sequence.
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