# Independence and Matching Numbers of Unicyclic Graphs From Null Space

## TL;DR

This paper characterizes singular unicyclic graphs using null space support and derives formulas for their independence and matching numbers, enabling linear algebra-based computations.

## Contribution

It introduces new formulas for independence and matching numbers of unicyclic graphs based on null space support, advancing graph theoretical analysis.

## Key findings

- Characterization of singular unicyclic graphs
- Closed-form formulas for independence and matching numbers
- Linear algebra methods for graph property computation

## Abstract

We characterize unicyclic graphs that are singular using the support of the null space of their pendant trees. From this, we obtain closed formulas for the independence and matching numbers of a unicyclic graph, based on the support of its subtrees. These formulas allows one to compute independence and matching numbers of unicyclic graphs using linear algebra methods.