Extremal Laplacian energy of $\overrightarrow{C_{k+1}}$-free digraphs

Xiuwen Yang, Lin-Peng Zhang

The Laplacian energy of a digraph $G$ is defined as ${\sum }_{i=1}^n\hat{I}{»}_i^2$, where $\hat{I}{»}_i$ are the eigenvalues of the Laplacian matrix of $G$. A (di)graph $G$ is said to be $H$-free i…