An upper bound on the nullity of signed graphs

TL;DR

This paper establishes an upper limit on the nullity of signed graphs based on their cyclomatic number and pendant vertices, and fully characterizes the extremal graphs achieving this bound.

Contribution

It provides a new upper bound on nullity for signed graphs and characterizes the extremal cases, advancing understanding of graph nullity in signed graph theory.

Findings

Derived an explicit upper bound on nullity involving cyclomatic number and pendant vertices.

Characterized all extremal signed graphs that attain this upper bound.

Abstract

In this paper, an upper bound on the nullity of signed graphs in terms of the cyclomatic number and the number of pendant vertices is proved, and the corresponding extremal signed graphs are completely characterized.