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Asymptotically Optimal Solutions for Small World Graphs

✍ Scribed by Michele Flammini; Luca Moscardelli; Alfredo Navarra; Stéphane Pérennes

Book ID
105914976
Publisher
Springer
Year
2007
Tongue
English
Weight
492 KB
Volume
42
Category
Article
ISSN
1433-0490

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📜 SIMILAR VOLUMES

An asymptotic formula for the number of
An asymptotic formula for the number of graphs having small diameter
✍ Ioan Tomescu 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 351 KB

In this paper it is shown that for every fixed k 1> 3, G(n; d = k) = 2(~) (6.2 -k + o(1))", where G(n; d = k) denotes the number of graphs of order n and diameter equal to k. It is also proved that for every fixed k>~2, lim,~G(n;d=k)/G(n;d=k+ 1)=lim.o~G(n;d=n-k)/ G(n;d=n-k+ 1)= oo hold.