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Diameters of random circulant graphs
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Combinatorica, ISSN 0209-9683, E-ISSN 1439-6912, Vol. 33, no 4, 429-466 p.Article in journal (Refereed) Published
Abstract [en]

The diameter of a graph measures the maximal distance between any pair of vertices. The diameters of many small-world networks, as well as a variety of other random graph models, grow logarithmically in the number of nodes. In contrast, the worst connected networks are cycles whose diameters increase linearly in the number of nodes. In the present study we consider an intermediate class of examples: Cayley graphs of cyclic groups, also known as circulant graphs or multi-loop networks. We show that the diameter of a random circulant 2k-regular graph with n vertices scales as n (1/k) , and establish a limit theorem for the distribution of their diameters. We obtain analogous results for the distribution of the average distance and higher moments.

Place, publisher, year, edition, pages
2013. Vol. 33, no 4, 429-466 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-214057DOI: 10.1007/s00493-013-2820-6ISI: 000327896300003OAI: oai:DiVA.org:uu-214057DiVA: diva2:683934
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council, 621-2007-6352
Available from: 2014-01-07 Created: 2014-01-07 Last updated: 2017-12-06Bibliographically approved

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Strömbergsson, Andreas

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