A characterization of signed planar graphs with rank at most 4

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:

• signed planar graphs
• adjacency matrix
• rank

AMS Subject Classifications:

• 05C05
• 05C50

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]’.