Iota energy orderings of bicyclic signed digraphs
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 $E(S)=\sum_{k=1}^n|{Re}(z_k)|$, where ${Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the eigenvalue of the adjacency matrix of $S$ with $n$ ve...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Isfahan
2021-09-01
|
| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | https://toc.ui.ac.ir/article_25567_b7b94ad4ded8b3949671f85716761580.pdf |
| _version_ | 1819104251846066176 |
|---|---|
| author | Xiuwen Yang Ligong Wang |
| author_facet | Xiuwen Yang Ligong Wang |
| author_sort | Xiuwen Yang |
| collection | DOAJ |
| description | 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 $E(S)=\sum_{k=1}^n|{Re}(z_k)|$, where ${Re}(z_k)$ 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 $E(S)=\sum_{k=1}^n|{Im}(z_k)|$, where ${Im}(z_k)$ 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. |
| first_indexed | 2024-12-22T02:03:23Z |
| format | Article |
| id | doaj.art-8d48f4866a264ecb8df342305dc61a42 |
| institution | Directory Open Access Journal |
| issn | 2251-8657 2251-8665 |
| language | English |
| last_indexed | 2024-12-22T02:03:23Z |
| publishDate | 2021-09-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | Transactions on Combinatorics |
| spelling | doaj.art-8d48f4866a264ecb8df342305dc61a422022-12-21T18:42:35ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652021-09-0110318720010.22108/toc.2021.126881.180525567Iota energy orderings of bicyclic signed digraphsXiuwen Yang0Ligong Wang1School of Mathematics and Statistics, Northwestern Polytechnical University, 710129, Xi’an, Shaanxi, P. R. ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, 710129, Xi’an, Shaanxi, P. R. ChinaThe 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 $E(S)=\sum_{k=1}^n|{Re}(z_k)|$, where ${Re}(z_k)$ 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 $E(S)=\sum_{k=1}^n|{Im}(z_k)|$, where ${Im}(z_k)$ 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.https://toc.ui.ac.ir/article_25567_b7b94ad4ded8b3949671f85716761580.pdforderingsiota energybicyclic signed digraphs |
| spellingShingle | Xiuwen Yang Ligong Wang Iota energy orderings of bicyclic signed digraphs Transactions on Combinatorics orderings iota energy bicyclic signed digraphs |
| title | Iota energy orderings of bicyclic signed digraphs |
| title_full | Iota energy orderings of bicyclic signed digraphs |
| title_fullStr | Iota energy orderings of bicyclic signed digraphs |
| title_full_unstemmed | Iota energy orderings of bicyclic signed digraphs |
| title_short | Iota energy orderings of bicyclic signed digraphs |
| title_sort | iota energy orderings of bicyclic signed digraphs |
| topic | orderings iota energy bicyclic signed digraphs |
| url | https://toc.ui.ac.ir/article_25567_b7b94ad4ded8b3949671f85716761580.pdf |
| work_keys_str_mv | AT xiuwenyang iotaenergyorderingsofbicyclicsigneddigraphs AT ligongwang iotaenergyorderingsofbicyclicsigneddigraphs |