On the skew spectral moments of graphs
نویسندگان
1 University of zanjan
2 Department of Mathematics, University of Zanjan
3 Department of Mathematics, University of Zanjan
doi
10.22108/toc.2017.20737چکیده
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 $T_k(G^{\sigma_1}_{1}) <T_k(G^{\sigma_ 2}_{2})$ then we write $G^{\sigma_1}_{1} \prec_{T} G^{\sigma_2}_{2}$. In this paper, we determine some of the skew spectral moments of oriented graphs. Also we order some oriented unicyclic graphs with respect to skew spectral moment.
