Further Properties of Reproducing Graphs

References

[1] P. Erd?s and A. Rényi, “On Random Graphs. I,” Publicationes Mathematicae, Vol. 6, 1959.

[2]
G. U. Yule, “A Mathematical Theory of Evolution, Based on the Conclusions of Dr. J. C. Willis, F.R.S.,” Philosophical Transactions of the Royal Society of London, London, Vol. B213, 1925, pp. 21-87.

[3]
R. Albert, A. Barabasi and H. Jeong, “Mean-Field Theory for Scale-Free Random Networks,” Physica A, Vol. 272, 1999, pp. 173-187.

[4]
M. Penrose, “Random Geometric Graphs,” Oxford University Press, Oxford, 2003.

[5]
D. J. Watts and S. H. Strogatz, “Collective Dynamics of ‘Small-World’ Networks,” Nature, Vol. 393, No. 6684, 1998, pp. 409-410.

[6] R. Southwell and C. Cannings, “Games on Graphs that Grow Determinis-Tically,” In: Proceedings of International Conference on Game Theory for Networks Game-Nets‘09, Istanbul, 2009, pp. 347-356.

[7]
R. Southwell and C. Cannings, “Some Models of Re- producing Graphs. 1 Pure Reproduction,” Under Review.

[8]
R. Southwell and C. Cannings, “Some Models of Reproducing Graphs. 2 Age Capped Vertices,” Under Review.

[9]
F. Chung, L. Lu, T. Dewey and D. Gales, “Duplication Models for Biological Networks,” Journal of Computational Biology, Vol. 10, 2003, pp. 677-687.

[10]
N. Cohen, J. Jordan and M. Voliotis, “Preferential Duplication Graphs,” Journal of Applied Probability, Vol. 47, No. 2, 2010, pp. 572-585.

[11] A. Bonato, N. Hadi, P. Horn, P. Pralat and C. Wang, “Models of on-Line Social Networks,” Internet Mathematics, 2010.

[12] N. J. A. Sloane, “The On-Line Encyclopedia of Integer Sequences,” 2009. http:www.research.att.com/njas/sequences/

[13]
N. J. A. Sloane and J. A. Sellers, “On Non-Squashing Partitions,” Discrete Mathematics, Vol. 294, No. 3, 2005, pp. 259-274.

[14]
J. B. Olsson, “Sign Conjugacy Classes in Symmetric Groups,” Journal of Algebra, Vol. 322, No. 8, 2009, pp. 2793-2800.