论文标题
Bicyclic签名的Digraphs的IOTA能量顺序
Iota energy orderings of bicyclic signed digraphs
论文作者
论文摘要
签名的挖掘物的能量概念扩展到了签名的挖掘物的IOTA能量。 The energy of a signed digraph $S$ is defined by $E(S)=\sum_{k=1}^n|\text{Re}(z_k)|$, where $\text{Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the eigenvalue of the adjacency matrix of $S$ with $n$ vertices, $ k = 1,2，\ ldots，n $。然后，$ s $的iota能量由$ e（s）= \ sum_ {k = 1}^n | \ text {im}（z_k）| $，其中$ \ text {im}（z_k）$是eigenvalue $ z_k $。在本文中，我们考虑了一个特殊的图形类，用于签名的Digraphs $ \ MATHCAL {S} _n $，带有$ n $顶点，该$ n $顶点具有两个顶点dischient签名的指向均匀的循环。我们给出了两种双环签名的挖掘物的IOTA能量顺序，一个包括两个正或两个负向的偶数循环，另一个包括一个正和一个负向的偶数循环。
The concept of energy of a signed digraph is extended to iota energy of a signed digraph. The energy of a signed digraph $S$ is defined by $E(S)=\sum_{k=1}^n|\text{Re}(z_k)|$, where $\text{Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the eigenvalue of the adjacency matrix of $S$ with $n$ vertices, $k=1,2,\ldots,n$. Then the iota energy of $S$ is defined by $E(S)=\sum_{k=1}^n|\text{Im}(z_k)|$, where $\text{Im}(z_k)$ is the imaginary part of eigenvalue $z_k$. In this paper, we consider a special graph class for bicyclic signed digraphs $\mathcal{S}_n$ with $n$ vertices which have two vertex-disjoint signed directed even cycles. We give two iota energy orderings of bicyclic signed digraphs, one is including two positive or two negative directed even cycles, the other is including one positive and one negative directed even cycles.
