半正则混合图的线图的谱

(集美大学理学院,福建 厦门 361021)

混合图; 半正则图; 线图; H-邻接矩阵;

Spectra of line graphs of semiregular mixed graphs
XIE Lingyan,YAN Weigen*

(School of Sciences,Jimei University,Xiamen 361021,China)

mixed graph; semiregular graph; line graph; Hermitain-adjacency matrix; spectra

DOI: 10.6043/j.issn.0438-0479.201809010

备注

给一个无向图的某些边定向得到的图称为混合图,它可能既存在无向边又存在有向边.一个无向半正则图G的线图l(G)的邻接谱完全由G的邻接谱确定.主要推广了前面这个结果,证明了半正则混合图G的线图l(G)的H-邻接谱完全由混合图G的H-邻接谱确定.

A mixed graph is obtained from an undirected graph G by orienting edges of some subset of the edge set of G. It is well known that the spectrum of the line graph of a semiregular undirected graph G is determined by the spectrum of G. In this work,we generalize this result and prove that the Hermitian adjacent spectrum of the line graph of a semiregular mixed graph G can be expressed completely by the one of G.