Mixed graphs with \(H\)-rank 3. (English) Zbl 1361.05076
Summary: B. Mohar [ibid. 489, 324–340 (2016; Zbl 1327.05215)] determined all mixed graphs with \(H\)-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 their \(H\)-spectrum. In the present paper, we investigate the \(H\)-rank of mixed graphs further, determining the \(H\)-ranks of those mixed graphs with trees, cycles and complete bipartite graphs as underlying graphs, respectively. Moreover, we characterize all mixed graphs with \(H\)-rank 3, and show that all connected mixed graphs with \(H\)-rank 3 can be determined by their \(H\)-spectrum.
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
Citations:
Zbl 1327.05215References:
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