More on the minimum skew-rank of graphs
Hui Yan Qu, Guihai Yu, Feng Li · Operators and Matrices · 2015
The minimum (maximum) skew-rank of a simple graph G over real field is the smallest (largest) possible rank among all skew-symmetric matrices over real field whose i j -th entry is nonzero whenever v i v j is an edge in G and is zero otherwise. In this paper we obtain more results about the minimum skew-rank of graphs. Further we get a lower (upper) bound for minimum (maximum) skew-rank of unicyclic graph of order n with girth k , and characterize unicyclic graphs attaining the extremal values. Moreover, we characterize the unicyclic graphs with skew-rank 4 or 6, respectively. Finally we consider the non-singularity of skew-symmetric matrices described by unicyclic graphs.