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Issue No. 01 - January-March (2006 vol. 3)
ISSN: 1545-5963
pp: 84-91
C. Semple , Dept. of Math. & Stat., Canterbury Univ., Christchurch
M. Steel , Dept. of Math. & Stat., Canterbury Univ., Christchurch
Graphs obtained from a binary leaf labeled ("phylogenetic") tree by adding an edge so as to introduce a cycle provide a useful representation of hybrid evolution in molecular evolutionary biology. This class of graphs (which we call "unicyclic networks") also has some attractive combinatorial properties, which we present. We characterize when a set of binary phylogenetic trees is displayed by a unicyclic network in terms of tree rearrangement operations. This leads to a triple-wise compatibility theorem and a simple, fast algorithm to determine 1-cycle compatibility. We also use generating function techniques to provide closed-form expressions that enumerate unicyclic networks with specified or unspecified cycle length, and we provide an extension to enumerate a class of multicyclic networks
Phylogeny, Displays, Tree graphs, Evolution (biology), Bioinformatics, Biological system modeling, Genomics, Steel, Closed-form solution, Biological processes

C. Semple and M. Steel, "Unicyclic networks: compatibility and enumeration," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. 1, pp. 84-91, 2008.
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