On the skew spectral moments of graphs
Let $G$ be a simple graph, and $G^{sigma}$ be an oriented graph of $G$ with the orientation $sigma$ and skew-adjacency matrix $S(G^{sigma})$. The $k-$th skew spectral moment of $G^{sigma}$, denoted by $T_k(G^{sigma})$, is defined as $sum_{i=1}^{n}( lambda_{i})^{k}$, where $lambda...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2017-03-01
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| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | http://toc.ui.ac.ir/article_20737_9c81a151b424aac06fc6253943dc89a2.pdf |
| Summary: | Let $G$ be a simple graph, and $G^{sigma}$ be an oriented graph of $G$ with the orientation $sigma$ and skew-adjacency matrix $S(G^{sigma})$. The $k-$th skew spectral moment of $G^{sigma}$, denoted by $T_k(G^{sigma})$, is defined as $sum_{i=1}^{n}( lambda_{i})^{k}$, where $lambda_{1}, lambda_{2},cdots, lambda_{n}$ are the eigenvalues of $G^{sigma}$. Suppose $G^{sigma_1}_{1}$ and $G^{sigma_2}_{2}$ are two digraphs. If there exists an integer $k$, $1 leq k leq n-1$, such that for each $i$, $0 leq i leq k-1$, $T_i(G^{sigma_1}_{1}) = T_i(G^{sigma_2}_{2})$ and $T_k(G^{sigma_1}_{1}) |
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| ISSN: | 2251-8657 2251-8665 |