On the Skew Spectral Moments of Trees and Unicyclic Graphs  

作　　者：Yaping WU Huiqing LIU Qiong FAN 

机构地区：[1]School of Artificial Intelligence,Jianghan University,Hubei 430056,P.R.China [2]School of Mathematics and Statistics,Hubei University,Hubei 430062,P.R.China [3]School of Mathematics and Statistics,Central China Normal University,Hubei 430079,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第4期389-398,共10页数学研究及应用（英文版）

基　　金：Supported by the Research Project of Jianghan University(Grant No.2021yb056);the National Natural Science Foundation of China(Grant Nos.11971158;12061039).

摘　　要：Given a simple graph G,the oriented graph G^(σ)is obtained from G by orienting each edge and G is called the underlying graph of G^(σ).The skew-symmetric adjacency matrix S(G^(σ))of G^(σ),where the(u,v)-entry is 1 if there is an arc from u to v,and−1 if there is an arc from v to u(and 0 otherwise),has eigenvalues of 0 or pure imaginary.The k-th-skew spectral moment of Gσis the sum of power k of all eigenvalues of S(G^(σ)),where k is a non-negative integer.The skew spectral moments can be used to produce graph catalogues.In this paper,we researched the skew spectral moments of some oriented trees and oriented unicyclic graphs and produced their catalogues in lexicographical order.We determined the last 2[d/4]oriented trees with underlying graph of diameter d and the last 2[g/4]+1 oriented unicyclic graphs with underlying graph of girth g,respectively.

关 键 词：oriented graph skew spectral moment TREE unicyclic graph 

分 类 号：O157.5[理学—数学]