Null Decomposition of Trees
Combinatorics
2017-08-04 v1
Abstract
Let be a tree, we show that the null space of the adjacency matrix of has relevant information about the structure of . 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