Signed distance Laplacian matrices for signed graphs

ABSTRACT

A signed graph is a graph whose edges are labelled either positive or negative. Corresponding to the two signed distance matrices defined for signed graphs, we define two signed distance Laplacian matrices. We characterize singularity and calculate the rank of these matrices and find signed distance Laplacian spectra of some classes of unbalanced signed graphs. We derive most of these results by proving them more generally for weighted signed graphs.

KEYWORDS:

• Signed graph
• signed distance matrix
• signed distance Laplacian matrix
• signed distance laplacian spectrum

MATHEMATICS SUBJECT CLASSIFICATIONS (2010):

• 05C12
• 05C22
• 05C50
• 05C75

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author would like to acknowledge her gratitude to Department of Science and Technology, Govt. of India for the financial support under INSPIRE Fellowship scheme Reg No: IF180462. The second author would like to acknowledge her gratitude to Science and Engineering Research Board (SERB), Govt. of India, for the financial support under the scheme Mathematical Research Impact Centric Support (MATRICS), vide order no.: File No. MTR/2017/000689.