The rank of a graph G is defined to be the rank of its adjacency matrix A(G). In this paper we characterize all connected triangle-free graphs with rank 6.
@article{arxiv.1301.0374,
title = {The triangle-free graphs with rank 6},
author = {Long Wang and Yi-Zheng Fan and Yi Wang},
journal= {arXiv preprint arXiv:1301.0374},
year = {2014}
}