A characterization of signed planar graphs with rank at most 4

作者:Tian, Fenglei; Wang, Dengyin*; Zhu, Min
来源:Linear and Multilinear Algebra, 2016, 64(5): 807-817.
DOI:10.1080/03081087.2015.1057137

摘要

A signed graph consists of an underlying graph and a sign function, which assigns each edge of a sign, either positive or negative. The adjacency matrix of a signed graph is defined as, where is the adjacency matrix of the underlying graph. The rank of is defined to be the rank of. In this paper, we characterize the signed graphs with rank or, and characterize the signed planar graphs with rank 4.