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Abstract
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
with
, 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.
Keywords:
Acknowledgements
The authors thank the referees for a careful and thorough reading of the paper and for valuable comments.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work was supported by ‘the National Natural Science Foundation of China [grant number 11171343]’.