S-trees

TL;DR

This paper introduces new graph operations and the concept of S-trees, enabling detailed analysis of adjacency matrices and matching structures in trees, with potential applications in graph theory and network analysis.

Contribution

It presents novel graph operations and the S-trees framework, providing a comprehensive method to analyze adjacency matrices and matchings in trees.

Findings

asis for all fundamental subspaces of adjacency matrices of trees

Detailed understanding of matching structures in trees

New graph operations facilitating these analyses

Abstract

In this paper two new graph operations are introduced, and with them the S-trees are studied in depth. This allows to find \(\{-1,0,1\}\)-basis for all the fundamental subspaces of the adjacency matrix of any tree, and to understand in detail the matching structure of any tree.