Article ID Journal Published Year Pages File Type
4647975 Discrete Mathematics 2013 9 Pages PDF
Abstract

In this paper it is proved that there are constants 0n−c2lognd>n−c2logn the typical graph has a completely different snakelike structure. The number of nn-vertex graphs of diameter dd is (1+o(1))12n(d+1)3n−d−1dn−d−1 whenever n→∞n→∞ and d>n−c2lognd>n−c2logn.

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Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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The structure of the typical graphs of given diameter
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