Mixed graphs with H-rank 3☆
Mixed graphs with H-rank 3☆
复制标题
DOI：
10.1016/j.laa.2017.02.037
复制
发表时间：
2017-07
影响因子：
1.1
通讯作者：
Yi Wang;Bo-Jun Yuan;Shuangdong Li;Chong-Jun Wang
中科院分区：
文献类型：
--
作者：
Yi Wang;Bo-Jun Yuan;Shuangdong Li;Chong-Jun Wang
在文章（Mohar，2016 [9]）中，Mohar确定了所有H-秩为2的混合图，并使用它来分类关于其Hermitian邻接矩阵的共谱图，构造了一类不能由其H-谱确定的图。本文进一步研究了混合图的H-秩，分别确定了以树、圈和完全二部图为基础图的混合图的H-秩。此外，我们还刻画了所有H-秩为3的混合图，并证明了所有H-秩为3的连通混合图都可以由它们的H-谱来确定。
In the article (Mohar, 2016 [9]), Mohar determined all mixed graphs withH-rank 2, and used it to classify cospectral graphs with respect to their Hermitian adjacency matrix, constructing a class of graphs which can not be determined by theirH-spectrum. In the present paper, we investigate theH-rank of mixed graphs further, determining theH-ranks of those mixed graphs with trees, cycles and complete bipartite graphs as underlying graphs, respectively. Moreover, we characterize all mixed graphs withH-rank 3, and show that all connected mixed graphs withH-rank 3 can be determined by theirH-spectrum.