# Null Decomposition of Unicyclic Graphs

## TL;DR

This paper extends the null decomposition technique from trees to unicyclic graphs, providing formulas for independence and matching numbers based on the graph's support.

## Contribution

It introduces a null decomposition for unicyclic graphs and derives formulas for key graph invariants using this approach.

## Key findings

- Null space basis for unicyclic graphs obtained.
- Closed formulas for independence and matching numbers derived.
- Extension of null decomposition from trees to unicyclic graphs.

## Abstract

In this work we obtain basis for the null space of unicyclic graphs. We extend the null decomposition of trees from [11] for unicyclic graphs. As an application, we obtain closed formulas for the independence and matching numbers of unicyclic graphs just using the support of the graph.

---
Source: https://tomesphere.com/paper/1907.08618