• Corpus ID: 219177437

# No signed graph with the nullity $\eta(G,\sigma)=|V(G)|-2m(G)+2c(G)-1$

@article{Lu2020NoSG,
title={No signed graph with the nullity \$\eta(G,\sigma)=|V(G)|-2m(G)+2c(G)-1\$},
author={Yong Lu and Jingwen Wu},
journal={arXiv: Combinatorics},
year={2020}
}
• Published 29 May 2020
• Mathematics
• arXiv: Combinatorics
Let $G^{\sigma}=(G,\sigma)$ be a signed graph and $A(G,\sigma)$ be its adjacency matrix. Denote by $m(G)$ the matching number of $G$. Let $\eta(G,\sigma)$ be the nullity of $(G,\sigma)$. He et al. [Bounds for the matching number and cyclomatic number of a signed graph in terms of rank, Linear Algebra Appl. 572 (2019), 273--291] proved that $$|V(G)|-2m(G)-c(G)\leq\eta(G,\sigma)\leq |V(G)|-2m(G)+2c(G),$$ where $c(G)$ is the dimension of cycle space of $G$. Signed graphs reaching the lower bound…

## References

SHOWING 1-10 OF 20 REFERENCES

• Mathematics
• 2016
The nullity of a graph G, denoted by η(G)$\eta(G)$, is the multiplicity of the eigenvalue zero of its adjacency matrix. In this paper, we determine all graphs with η(G)=n(G)−2m(G)−c(G)\$\eta(G)=n(G) -
• Chen Chen
• Mathematics
• 2018
Abstract A mixed graph is obtained by orienting some edges of G, where G is the underlying graph of . Let denote the Hermitian adjacency matrix of and m(G) be the matching number of G. The H-rank of