{"title":"关于图的偏谱矩","authors":"F. Taghvaee, G. Fath-Tabar","doi":"10.22108/TOC.2017.20737","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"47-54"},"PeriodicalIF":0.6000,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the skew spectral moments of graphs\",\"authors\":\"F. Taghvaee, G. Fath-Tabar\",\"doi\":\"10.22108/TOC.2017.20737\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":43837,\"journal\":{\"name\":\"Transactions on Combinatorics\",\"volume\":\"6 1\",\"pages\":\"47-54\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2017-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2017.20737\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2017.20737","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设$G$是一个简单图，$G^{sigma}$ $是$G$的一个有向图，有向$sigma$和斜邻接矩阵$S(G^{sigma})$ $。的k - th美元倾斜光谱时刻$ G ^{σ}$用T_k美元(G ^{σ})$被定义为美元sum_ {i = 1} ^ {n}(lambda_{我})^ {k} $,美元lambda_{1},lambda_ {2}, cdots,lambda_ {n} $的特征值是$ G ^{σ}$。假设$ G ^ {sigma_1} _{1} $和$ G ^ {sigma_2} _{2} $是两个有向图。如果存在整数k美元,1 leq k leq n - 1美元,每个这样我美元,0 leq我leq k - 1美元,T_i美元(G ^ {sigma_1} _{1}) =T_i (G ^ {sigma_2} _{2})和美元T_k美元(G ^ {sigma_1} _ {1}) < T_k (G ^ {sigma_ 2} _{2})美元然后写$ G ^ {sigma_1} _ {1} prec_ {T} G ^ {sigma_2} _{2} $。在本文中，我们确定了一些有向图的偏谱矩。我们还对一些关于偏谱矩的有向单环图进行了排序。
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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