On Extremal p-Energy of Bicyclic Digraphs

The <i>p</i>-energy of a <i>k</i>-vertex digraph <i>D</i> is defined by Ep(D)=∑j=1k|R(λj)I(λj)|, where λ1,…,λk are eigenvalues of <i>D</i> and R(λj) and I(λj) are respectively real and imaginary parts of the eigenvalue λj. In the present paper, we consider a class of bicyclic digraphs such that each digraph in this class contains two vertex-disjoint directed cycles. We find digraphs in this class with extremal <i>p</i>-energy.

$k$顶点有向图$D$的p-能量（p-energy）定义为$E_p(D)=sum_{j=1}^k |R(lambda_j)I(lambda_j)|$，其中$lambda_1,dots,lambda_k$为$D$的特征值，$R(lambda_j)$与$I(lambda_j)$分别为特征值$lambda_j$的实部与虚部。本文研究一类双圈有向图，该类中的每个有向图均包含两个顶点不相交的有向环。我们找到了该类中具有极值p-能量的有向图。