A characterization of graphs with rank 5

A note on the nullity of unicyclic signed graphs

“…Cheng and Liu [3] characterize the graphs of order n with nullity n − 2 or n − 3. Cheng et al [4,5] characterize the graphs of order n with nullity n − 4 or n − 5. More results on the nullity (or rank) of graphs can be found in the book [28] and the paper [31].…”

Bipartite graphs with at most six non-zero eigenvalues

“…It is not hard to characterize the reduced graphs with rank r, for r ≤ 3. The classification of reduced graphs of rank 4 and rank 5 can be found in [8] and also in [1] and [2], respectively. Thus it is natural to classify all reduced graphs of rank 6 ( see [8] for a characterization according to minimal subgraphs of nullity one).…”

On bipartite graphs which attain minimum rank among bipartite graphs with given diameter

“…Fan and Qian [10] characterized all bipartite graphs with rank 4. Recently Chang, Huang, and Yeh characterized the graphs with rank 4 in [4] and also the graphs with rank 5 in [5]. Other works on the rank or nullity of graphs can be found in [2,12,14,15,16,17,18,19,20].…”