Oriented unicyclic graphs with extremal skew energy

TL;DR

This paper characterizes oriented unicyclic graphs that have the smallest and largest skew energy by analyzing their eigenvalues, contributing to spectral graph theory.

Contribution

It identifies the specific unicyclic graphs that maximize or minimize skew energy among all oriented unicyclic graphs.

Findings

Determined the unicyclic graphs with minimal skew energy.

Identified the unicyclic graphs with maximal skew energy.

Provided spectral characterizations of extremal graphs.

Abstract

Let $\G$ be an oriented graph of order $n$ and $\a_1,\a_2,..., \a_n$ denote all the eigenvalues of the skew-adjacency matrix of $\G.$ The skew energy $\displaystyle{\cal E}_s(\G)= \sum_{i=1}^{n} |\a_i|.$ In this paper, the oriented unicyclic graphs with minimal and maximal skew energy are determined.