An Extension of the Prüfer Code and Assembly of Connected Graphs from Their Blocks

@article{Kajimoto2003AnEO,
  title={An Extension of the Pr{\"u}fer Code and Assembly of Connected Graphs from Their Blocks},
  author={Hiroshi Kajimoto},
  journal={Graphs and Combinatorics},
  year={2003},
  volume={19},
  pages={231-239}
}
Abstract. We give an extension of the Prüfer code in order to count connected labeled graphs whose blocks are of given type. The Prüfer code records the way of assembling a connected labeled graph from its blocks. 
Random graphs from a block-stable class
Random graphs from a block class
TLDR
It is shown that, as for trees, for most random n-vertex graphs in such a class, each vertex is in at most (1+o(1)log n/ log log n blocks, and each path passes through at most 5(n log n)^{1/2} blocks.
Learning Graphs From Linear Measurements: Fundamental Trade-Offs and Applications
TLDR
A three-stage recovery scheme for reconstructing a symmetric matrix that represents an underlying graph using linear measurements is considered, and experiments show that the heuristic algorithm outperforms basis pursuit on star graphs and applies to learn admittance matrices in electric grids.

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