Lower bound of the energy of a complex unit gain graph in terms of the matching number of its underlying graph

TL;DR

This paper derives a lower bound for the energy of complex unit gain graphs based on the matching number of their underlying graphs and characterizes those graphs that attain this bound.

Contribution

It introduces a new lower bound for the energy of complex unit gain graphs and characterizes the extremal graphs achieving this bound.

Findings

Established a lower bound for graph energy in terms of matching number.

Characterized all graphs that reach the energy bound.

Provides insights into the spectral properties of complex unit gain graphs.

Abstract

We establish a lower bound for the energy of a complex unit gain graph in terms of the matching number of its underlying graph, and characterize all the complex unit gain graphs whose energy reaches this bound.