English

Null Decomposition of Trees

Combinatorics 2017-08-04 v1

Abstract

Let TT be a tree, we show that the null space of the adjacency matrix of TT has relevant information about the structure of TT. We introduce the Null Decomposition of trees, and use it in order to get formulas for independence number and matching number of a tree. We also prove that the number of maximum matchings in a tree is related to the null decomposition.

Keywords

Cite

@article{arxiv.1708.00934,
  title  = {Null Decomposition of Trees},
  author = {Daniel A. Jaume and Gonzalo Molina},
  journal= {arXiv preprint arXiv:1708.00934},
  year   = {2017}
}

Comments

23 pages, 6 figures

R2 v1 2026-06-22T21:05:11.032Z