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.

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.Expand

IEEE Transactions on Signal and Information Processing over Networks

2020

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.Expand

Proceedings of the National Academy of Sciences of the United States of America

1956

2 The abbreviation "i.o." indicates "infinitely often," that is, for infinitely many i. Similarly, in equations (6) and (16) it indicates that every point of C is covered by infinitely many Ai. 3 In… Expand