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.

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.